**Minimizing disease spread on a quarantined cruise ship: A model of COVID-19 with asymptomatic infections.**

Abstract
On February 5 the Japanese government ordered the passengers and crew on the Diamond Princess to start a two week quarantine after a former passenger tested positive for COVID-19. During the quarantine the virus spread rapidly throughout the ship. By February 20, there were 651 cases. We model this quarantine with a SEIR model including asymptomatic infections with differentiated shipboard roles for crew and passengers. The study includes the derivation of the basic reproduction number and simulation studies showing the effect of quarantine with COVID-19 or influenza on the total infection numbers. We sho...

**Source: **Mathematical Biosciences - August 7, 2020 **Category: **Statistics **Authors: **Batista B, Dickenson D, Gurski K, Kebe M, Rankin N **Tags: **Math Biosci **Source Type: **research

**Modeling the viral dynamics of SARS-CoV-2 infection.**

Abstract
Coronavirus disease 2019 (COVID-19), an infectious disease caused by the infection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is spreading and causing the global coronavirus pandemic. The viral dynamics of SARS-CoV-2 infection have not been quantitatively investigated. In this paper, we use mathematical models to study the pathogenic features of SARS-CoV-2 infection by examining the interaction between the virus, cells and immune responses. Models are fit to the data of SARS-CoV-2 infection in patients and non-human primates. Data fitting and numerical simulation show that viral dyna...

**Source: **Mathematical Biosciences - August 6, 2020 **Category: **Statistics **Authors: **Wang S, Pan Y, Wang Q, Miao H, Brown AN, Rong L **Tags: **Math Biosci **Source Type: **research

**Modeling the transmission dynamics of the COVID-19 Pandemic in South Africa.**

This study is based on the use of a compartmental model to analyse the transmission dynamics of the disease in South Africa. A notable feature of the model is the incorporation of the role of environmental contamination by COVID-infected individuals. The model, which is fitted and parametrized using cumulative mortality data from South Africa, is used to assess the impact of various control and mitigation strategies. Rigorous analysis of the model reveals that its associated continuum of disease-free equilibria is globally-asymptotically stable whenever the control reproduction number is less than unity. The epidemiologica...

**Source: **Mathematical Biosciences - August 4, 2020 **Category: **Statistics **Authors: **Garba SM, Lubuma JM, Tsanou B **Tags: **Math Biosci **Source Type: **research

**Simulating COVID-19 in a university environment.**

Abstract
Residential colleges and universities face unique challenges in providing in-person instruction during the COVID-19 pandemic. Administrators are currently faced with decisions about whether to open during the pandemic and what modifications of their normal operations might be necessary to protect students, faculty and staff. There is little information, however, on what measures are likely to be most effective and whether existing interventions could contain the spread of an outbreak on campus. We develop a full-scale stochastic agent-based model to determine whether in-person instruction could safely con...

**Source: **Mathematical Biosciences - August 3, 2020 **Category: **Statistics **Authors: **Gressman PT, Peck JR **Tags: **Math Biosci **Source Type: **research

**Predicting COVID-19 spread in the face of control measures in West-Africa.**

RG
Abstract
The novel coronavirus (COVID-19) pandemic is causing devastating demographic, social, and economic damage globally. Understanding current patterns of the pandemic spread and forecasting its long-term trajectory is essential in guiding policies aimed at curtailing the pandemic. This is particularly important in regions with weak economies and fragile health care systems such as West-Africa. We formulate and use a deterministic compartmental model to (i) assess the current patterns of COVID-19 spread in West-Africa, (ii) evaluate the impact of currently implemented control measures, and (iii) predict th...

**Source: **Mathematical Biosciences - July 29, 2020 **Category: **Statistics **Authors: **Taboe HB, Salako KV, Tison JM, Ngonghala CN, Kakaï RG **Tags: **Math Biosci **Source Type: **research

**When is SARS-CoV-2 in your shopping list?**

This study may guide novel strategies for the mitigation of the current COVID-19 pandemic, at any stage, and prevention of future outbreaks of SARS-CoV-2 or related viruses.
PMID: 32730811 [PubMed - as supplied by publisher] (Source: Mathematical Biosciences)

**Source: **Mathematical Biosciences - July 27, 2020 **Category: **Statistics **Authors: **Hernandez-Mejia G, Hernandez-Vargas EA **Tags: **Math Biosci **Source Type: **research

**Dynamics of a two-sex model for the population ecology of dengue mosquitoes in the presence of Wolbachia.**

In this study, a new two-sex mathematical model for the population ecology of dengue mosquitoes and disease is designed and used to assess the population-level impact of the periodic release of Wolbachia-infected mosquitoes. Rigorous analysis of the model, which incorporates many of the lifecycle features of dengue disease and the cytoplasmic incompatibility property of Wolbachia bacterium in mosquitoes, reveal that the disease-free equilibrium of the model is locally-asymptotically stable whenever a certain epidemiological threshold, known as the reproduction number of the model (denoted by R0W), is less than unity. The m...

**Source: **Mathematical Biosciences - July 23, 2020 **Category: **Statistics **Authors: **Taghikhani R, Sharomi O, Gumel AB **Tags: **Math Biosci **Source Type: **research

**Inference on an heteroscedastic Gompertz tumor growth model.**

érez JJ, Torres-Ruiz F
Abstract
We consider a non homogeneous Gompertz diffusion process whose parameters are modified by generally time-dependent exogenous factors included in the infinitesimal moments. The proposed model is able to describe tumor dynamics under the effect of anti-proliferative and/or cell death-induced therapies. We assume that such therapies can modify also the infinitesimal variance of the diffusion process. An estimation procedure, based on a control group and two treated groups, is proposed to infer the model by estimating the constant parameters and the time-dependent terms. Moreover...

**Source: **Mathematical Biosciences - July 23, 2020 **Category: **Statistics **Authors: **Albano G, Giorno V, Román-Román P, Román-Román S, Serrano-Pérez JJ, Torres-Ruiz F **Tags: **Math Biosci **Source Type: **research

**Parameter estimation and experimental design for Hill-type muscles: Impulses from optimization-based modeling.**

z T
Abstract
The benefits of optimization-based modeling for parameter estimation of Hill-type muscle models are demonstrated. Therefore, we examined the model and data of Günther et al. (2007), who analyzed isometric, concentric, and quick-release contractions of a piglet calf muscle. We found that the isometric experiments are suitable for derivative-based parameter estimation while the others did not provide any additional value. During the estimation process, certain parameters had to be fixed. We give possible reasons and provide impulses for modelers. Subsequently, unnecessarily complex or deprecat...

**Source: **Mathematical Biosciences - July 22, 2020 **Category: **Statistics **Authors: **Rockenfeller R, Herold JL, Götz T **Tags: **Math Biosci **Source Type: **research

**A mathematical model of skeletal muscle regeneration with upper body vibration.**

This study investigates the effect that upper body vibration has on the recovery rate of the biceps muscle. A mathematical model that accounts for vibration is developed by adapting three vibration terms into the Stephenson and Kojourahov skeletal muscle regeneration mathematical model. The first term accounts for the increase in the influx rate of type 1 macrophages (P1). These cells are part of the body's immune response to muscle damage. They control the proliferation rate of satellite cells (S) and phagocytize dead myofiber cells. The second term accounts for the rate of the phenotype change of P1 to type 2 macrophages...

**Source: **Mathematical Biosciences - July 15, 2020 **Category: **Statistics **Authors: **Jones G, Smallwood C, Ruchti T, Blotter J, Feland B **Tags: **Math Biosci **Source Type: **research

**Application of the Goodwin model to autoregulatory feedback for stochastic gene expression.**

Abstract
In this paper we analyse stochastic expression of a single gene with its dynamics given by the classical Goodwin model with mRNA and protein contribution. We compare the effect of the presence of positive and negative feedback on the transcription regulation. In such cases we observe two qualitatively different types of asymptotic behaviour. In the case of a negative feedback loop, under sufficient conditions, one can find a stationary density for mRNA and protein molecules. In the case of a positive feedback loop we observe extinction of both types of molecules with time.
PMID: 32628944 [PubMed - as...

**Source: **Mathematical Biosciences - July 3, 2020 **Category: **Statistics **Authors: **Kozdęba A, Tomski A **Tags: **Math Biosci **Source Type: **research

**A structural-based computational model of tendon-bone insertion tissues.**

Abstract
Tendon-to-bone insertion provides a gradual transition from soft tendon to hard bone tissue, functioning to alleviate stress concentrations at the junction of these tissues. Such macroscopic mechanical properties are achieved due to the internal structure in which collagen fibers and mineralization levels are key ingredients. We develop a structural-based model of tendon-to-bone insertion incorporating such details as fiber preferred orientation, fiber directional dispersion, mineralization level, and their inhomogeneous spatial distribution. A python script is developed to alter the tapered tendon-bone t...

**Source: **Mathematical Biosciences - July 2, 2020 **Category: **Statistics **Authors: **Kuznetsov S, Pankow M, Peters K, Huang HS **Tags: **Math Biosci **Source Type: **research

**Global redistribution and local migration in semi-discrete host-parasitoid population dynamic models.**

Abstract
Host-parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving ordinary differential equations that mechanistically describe interactions when hosts become vulnerable to parasitoid attacks. We use this semi-discrete formalism to study two key spatial effects: local movement (migration) of parasitoids between patches during the vulnerable period; and yearly redistribution of populations across patches outside the vulnerable period. O...

**Source: **Mathematical Biosciences - June 29, 2020 **Category: **Statistics **Authors: **Emerick B, Singh A, Chhetri SR **Tags: **Math Biosci **Source Type: **research

**Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference.**

Abstract
Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the mutual interference exponent, and prey refuge, on the behavior of a predator-prey model with a generalized Holling type functional response - considering in particular the "non- smooth" case. This model can also be used to model an infectious disease where a susceptible population, moves to an infected class, after being infected by the disease. We ...

**Source: **Mathematical Biosciences - June 18, 2020 **Category: **Statistics **Authors: **Antwi-Fordjour K, Parshad RD, Beauregard MA **Tags: **Math Biosci **Source Type: **research

**Staggered release policies for COVID-19 control: Costs and benefits of relaxing restrictions by age and risk.**

Abstract
Lockdown and social distancing restrictions have been widely used as part of policy efforts aimed at controlling the ongoing COVID-19 pandemic. Since these restrictions have a negative impact on the economy, there exists a strong incentive to relax these policies while protecting public health. Using a modified SEIR epidemiological model, this paper explores the costs and benefits associated with the sequential release of specific groups based on age and risk from isolation. The results in this paper suggest that properly designed staggered-release policies can do better than simultaneous-release policies...

**Source: **Mathematical Biosciences - June 18, 2020 **Category: **Statistics **Authors: **Zhao H, Feng Z **Tags: **Math Biosci **Source Type: **research

**An explicitly multi-component arterial gas embolus dissolves much more slowly than its one-component approximation.**

Abstract
We worked out the growth and dissolution rates of an arterial gas embolism (AGE), to illustrate the evolution over time of its size and composition, and the time required for its total dissolution. We did this for a variety of breathing gases including air, pure oxygen, Nitrox and Heliox (each over a range of oxygen mole fractions), in order to assess how the breathing gas influenced the evolution of the AGE. The calculations were done by numerically integrating the underlying rate equations for explicitly multi-component AGEs, that contained a minimum of three (water, carbon dioxide and oxygen) and a max...

**Source: **Mathematical Biosciences - June 1, 2020 **Category: **Statistics **Authors: **Goldman S, Solano-Altamirano JM **Tags: **Math Biosci **Source Type: **research

**A data-driven network model for the emerging COVID-19 epidemics in Wuhan, Toronto and Italy.**

Abstract
The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modelling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the reported data ...

**Source: **Mathematical Biosciences - June 1, 2020 **Category: **Statistics **Authors: **Xue L, Jing S, Miller JC, Sun W, Li H, Estrada-Franco JG, Hyman JM, Zhu H **Tags: **Math Biosci **Source Type: **research

**Effects of periodic intake of drugs of abuse (morphine) on HIV dynamics: Mathematical model and analysis.**

In this study, we develop a mathematical model to analyze the effects of periodic intake of morphine, a widely used opiate. We consider two routes of morphine intake, namely, intravenous morphine (IVM) and slow-release oral morphine (SROM), and integrate several morphine pharmacodynamic parameters into HIV dynamics model. Using our non-autonomous model system we formulate the infection threshold, Ri, for global stability of infection-free equilibrium, which provides a condition for avoiding viral infection in a host. We demonstrate that the infection threshold highly depends on the morphine pharmacodynamic parameters. Such...

**Source: **Mathematical Biosciences - May 30, 2020 **Category: **Statistics **Authors: **Mutua JM, Wang FB, Vaidya NK **Tags: **Math Biosci **Source Type: **research

**On the benefits of flattening the curve: A perspective.**

Abstract
The many variations on a graphic illustrating the impact of non-pharmaceutical measures to mitigate pandemic influenza that have appeared in recent news reports about COVID-19 suggest a need to better explain the mechanism by which social distancing reduces the spread of infectious diseases. And some reports understate one benefit of reducing the frequency or proximity of interpersonal encounters, a reduction in the total number of infections. In hopes that understanding will increase compliance, we describe how social distancing a) reduces the peak incidence of infections, b) delays the occurrence of thi...

**Source: **Mathematical Biosciences - May 27, 2020 **Category: **Statistics **Authors: **Feng Z, Glasser JW, Hill AN **Tags: **Math Biosci **Source Type: **research

**Delay stability of reaction systems.**

Abstract
Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition for absolute delay stability of equilibrium concentrations, i.e., local asymptotic stability independent of the delay parameters. Several interesting examples on sequestration networks with delays are presented.
PMID: 32470445 [PubMed - as supplied by publisher] (Source: Mathematical Biosciences)

**Source: **Mathematical Biosciences - May 26, 2020 **Category: **Statistics **Authors: **Craciun G, Mincheva M, Pantea C, Yu PY **Tags: **Math Biosci **Source Type: **research

**Global dynamics of healthy and cancer cells competing in the hematopoietic system.**

n JT
Abstract
Stem cells in the bone marrow differentiate to ultimately become mature, functioning blood cells through a tightly regulated process (hematopoiesis) including a stem cell niche interaction and feedback through the immune system. Mutations in a hematopoietic stem cell can create a cancer stem cell leading to a less controlled production of malfunctioning cells in the hematopoietic system. This was mathematically modelled by Andersen et al. (2017) including the dynamic variables: healthy and cancer stem cells and mature cells, dead cells and an immune system response. Here, we apply a quasi steady...

**Source: **Mathematical Biosciences - May 19, 2020 **Category: **Statistics **Authors: **Andersen M, Hasselbalch HC, Kjær L, Skov V, Ottesen JT **Tags: **Math Biosci **Source Type: **research

**Modeling the impact of mass influenza vaccination and public health interventions on COVID-19 epidemics with limited detection capability.**

Abstract
The emerging coronavirus SARS-CoV-2 has caused a COVID-19 pandemic. SARS-CoV-2 causes a generally mild, but sometimes severe and even life-threatening infection, known as COVID-19. Currently, there exist no effective vaccines or drugs and, as such, global public authorities have so far relied upon non pharmaceutical interventions (NPIs). Since COVID-19 symptoms are aspecific and may resemble a common cold, if it should come back with a seasonal pattern and coincide with the influenza season, this would be particularly challenging, overwhelming and straining the healthcare systems, particularly in resource...

**Source: **Mathematical Biosciences - May 16, 2020 **Category: **Statistics **Authors: **Li Q, Tang B, Bragazzi NL, Xiao Y, Wu J **Tags: **Math Biosci **Source Type: **research

**Increase hemoglobin level in severe malarial anemia while controlling parasitemia: A mathematical model.**

Abstract
Macrophage migration inhibitory factor (MIF) is a pleiotropic cytokine produced by immune cells; it can play a protective or deleterious role in response to pathogens. The intracellular malaria parasite secretes a similar protein, PMIF. The present paper is concerned with severe malarial anemia (SMA), where MIF suppresses the recruitment of red blood cells (RBCs) from the spleen and the bone marrow. This suppression results in a decrease of the hemoglobin (Hb) in the blood to a dangerous level. Indeed, SMA is responsible for the majority of death-related malaria cases. Artesunate is the first line of trea...

**Source: **Mathematical Biosciences - May 13, 2020 **Category: **Statistics **Authors: **Siewe N, Friedman A **Tags: **Math Biosci **Source Type: **research

**Small binding-site clearance delays are not negligible in gene expression modeling.**

Abstract
During the templated biopolymerization processes of transcription and translation, a macromolecular machine, either an RNA polymerase or a ribosome, binds to a specific site on the template. Due to the sizes of these enzymes, there is a waiting time before one clears the binding site and another can bind. These clearance delays are relatively short, and one might think that they could be neglected. However, in the case of transcription, these clearance delays are associated with conservation laws, resulting in surprisingly large effects on the bifurcation diagrams in models of gene expression networks. We...

**Source: **Mathematical Biosciences - May 12, 2020 **Category: **Statistics **Authors: **Trofimenkoff EAM, Roussel MR **Tags: **Math Biosci **Source Type: **research

**Modeling behavioral change and COVID-19 containment in Mexico: A trade-off between lockdown and compliance.**

ez JX
Abstract
Sanitary Emergency Measures (SEM) were implemented in Mexico on March 30th, 2020 requiring the suspension of non-essential activities. This action followed a Healthy Distance Sanitary action on March 23rd, 2020. The aim of both measures was to reduce community transmission of COVID-19 in Mexico by lowering the effective contact rate. Using a modification of the Kermack-McKendrick SEIR model we explore the effect of behavioral changes required to lower community transmission by introducing a time-varying contact rate, and the consequences of disease spread in a population subject to suspension of non...

**Source: **Mathematical Biosciences - May 6, 2020 **Category: **Statistics **Authors: **Acuña-Zegarra MA, Santana-Cibrian M, Velasco-Hernandez JX **Tags: **Math Biosci **Source Type: **research

**Impact of venereal transmission on the dynamics of vertically transmitted viral diseases among mosquitoes.**

Abstract
Despite centuries of enormous control efforts, mosquito-borne diseases continue to show upward trend of morbidity. According to WHO reports, malaria caused 438000 deaths in the year 2015 and dengue cases has been increased 30-fold over the last five decades. To control these diseases, it is necessary to understand the transmission dynamics of them among mosquitoes. There are some vertically transmitted mosquito-borne diseases which can also be spread among mosquitoes through sexual contact (e.g., dengue, zika, chikungunya). Recent experimental observations indicate that for virus persistence in mosquito p...

**Source: **Mathematical Biosciences - May 5, 2020 **Category: **Statistics **Authors: **Nadim SS, Ghosh I, Martcheva M, Chattopadhyay J **Tags: **Math Biosci **Source Type: **research

**Crossover in spreading behavior due to memory in population dynamics.**

Abstract
The reaction-diffusion equation is one of the possible ways for modeling animal movement, where the reactive part stands for the population growth and the diffusive part for random dispersal of the population. However, a reaction-diffusion model may not represent all aspects of the spatial dynamics, because of the existence of distinct mechanisms that can affect the movement, such as spatial memory, which results in a bias for one direction of dispersal. This bias is modeled through an advective term on an advection-reaction-diffusion equation. Thus, considering the effects of memory on the population spr...

**Source: **Mathematical Biosciences - May 1, 2020 **Category: **Statistics **Authors: **Oliveira KA, Berbert JM **Tags: **Math Biosci **Source Type: **research

**Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus.**

This study shows that early termination of the strict social-distancing measures could trigger a devastating second wave with burden similar to those projected before the onset of the strict social-distancing measures were implemented. The use of efficacious face-masks (such as surgical masks, with estimated efficacy ≥ 70%) in public could lead to the elimination of the pandemic if at least 70% of the residents of New York state use such masks in public consistently (nationwide, a compliance of at least 80% will be required using such masks). The use of low efficacy masks, such as cloth masks (of estimated efficacy less...

**Source: **Mathematical Biosciences - April 30, 2020 **Category: **Statistics **Authors: **Ngonghala CN, Iboi E, Eikenberry S, Scotch M, MacIntyre CR, Bonds MH, Gumel AB **Tags: **Math Biosci **Source Type: **research

**An exact and implementable computation of the final outbreak size distribution under Erlang distributed infectious period.**

uml;rmann W
Abstract
This paper deals with a stochastic SIR (Susceptible-Infected-Recovered) model with Erlang(k,μ) distributed infectious period commonly referred as SIkR model. We show that using the total number of remaining Erlang stages as the state variable, we do not need to keep track of the stages of individual infections, and can employ a first step analysis to efficiently obtain quantities of interest. We study the distribution of the total number of recovered individuals and the distribution of the maximum number of individuals who are simultaneously infected until the end of the disease. In the lit...

**Source: **Mathematical Biosciences - April 30, 2020 **Category: **Statistics **Authors: **İşlier ZG, Güllü R, Hörmann W **Tags: **Math Biosci **Source Type: **research

**Complexity results for autocatalytic network models.**

Abstract
A key step in the origin of life is the emergence of a primitive metabolism. This requires the formation of a subset of chemical reactions that is both self-sustaining and collectively autocatalytic. A generic approach to study such processes ('RAF theory') has provided a precise and computationally effective way to address these questions, both on simulated data and in laboratory studies. In this paper, we solve some questions posed in more recent papers concerning the computational complexity of some key questions in RAF theory. In particular, although there is a fast algorithm to determine whether or n...

**Source: **Mathematical Biosciences - April 30, 2020 **Category: **Statistics **Authors: **Weller-Davies O, Steel M, Hein J **Tags: **Math Biosci **Source Type: **research

**Cost Analysis of Treatment Strategies for the Control of HSV-2 Infection in the U.S.: A Mathematical Modeling-Based Case Study.**

In this study, we develop and analyze a mathematical model to study the transmission and control of HSV-2 among the U.S. population between the ages of 15-49 when there are options to treat individuals in different stages of their pathogenicity. In particular, the goals of this work are to study the effect on HSV-2 transmission dynamics and to evaluate and compare the cost effectiveness of treating HSV-2 infections in both constitutional and non-constitutional stages (new strategy) against the current conventional treatment protocol for treating patients in the non-constitutional stage (current strategy). Our results disti...

**Source: **Mathematical Biosciences - April 28, 2020 **Category: **Statistics **Authors: **Almonte-Vega L, Colón-Vargas M, Luna-Jarrín L, Martinez J, Rodriguez-Rincón J, Murillo AL, Thakur M, Espinoza B, Patil R, Arriola L, Arunachalam V, Mubayi A **Tags: **Math Biosci **Source Type: **research

**The Quasi-State-State Approximations revisited: Timescales, small parameters, singularities, and normal forms in enzyme kinetics.**

Abstract
In this work, we revisit the scaling analysis and commonly accepted conditions for the validity of the standard, reverse and total quasi-steady-state approximations through the lens of dimensional Tikhonov-Fenichel parameters and their respective critical manifolds. By combining Tikhonov-Fenichel parameters with scaling analysis and energy methods, we derive improved upper bounds on the approximation error for the standard, reverse and total quasi-steady-state approximations. Furthermore, previous analyses suggest that the reverse quasi-steady-state approximation is only valid when initial enzyme concentr...

**Source: **Mathematical Biosciences - March 14, 2020 **Category: **Statistics **Authors: **Eilertsen J, Schnell S **Tags: **Math Biosci **Source Type: **research

**An efficient procedure to assist in the re-parametrization of structurally unidentifiable models.**

Abstract
An efficient method that assists in the re-parametrization of structurally unidentifiable models is introduced. It significantly reduces computational demand by combining both numerical and symbolic identifiability calculations. This hybrid approach facilitates the re-parametrization of large unidentifiable ordinary differential equation models, including models where state transformations are required. A model is first assessed numerically, to discover potential structurally unidentifiable parameters. Then, we use symbolic calculations to confirm the numerical results, after which we describe the algebra...

**Source: **Mathematical Biosciences - March 11, 2020 **Category: **Statistics **Authors: **Joubert D, Stigter JD, Molenaar J **Tags: **Math Biosci **Source Type: **research

**A new approach to simulating stochastic delayed systems.**

Abstract
In this paper we present a new method for deriving Itô stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME, we prove that they are equivalent both in distribution, and in sample paths they produce. This allows us to formulate an algorithmic approach to deriving equivalent Itô SDDEs with a smaller number of noise variables, which increases the computational speed of simulating stochastic delayed systems. The new method is illustrated on a simple model of two interacti...

**Source: **Mathematical Biosciences - February 27, 2020 **Category: **Statistics **Authors: **Fatehi F, Kyrychko YN, Blyuss KB **Tags: **Math Biosci **Source Type: **research

**Modelling Triatomine Bug Population and Trypanosoma rangeli Transmission Dynamics: Co-feeding, Pathogenic Effect and Linkage with Chagas Disease.**

Abstract
Trypanosoma rangeli (T. rangeli), a parasite, is not pathogenic to human but pathogenic to some vector species to induce the behavior changes of infected vectors and subsequently impact the transmission dynamics of other diseases such as Chagas disease which shares the same vector species. Here we develop a mathematical model and conduct qualitative analysis for the transmission dynamics of T. rangeli. We incorporate both systemic and co-feeding transmission routes, and account for the pathogenic effect using infection-induced fecundity and fertility change of the triatomine bugs. We derive two thresholds...

**Source: **Mathematical Biosciences - February 21, 2020 **Category: **Statistics **Authors: **Wu X, Gao D, Song Z, Wu J **Tags: **Math Biosci **Source Type: **research

**Modelling and control of a banana soilborne pest in a multi-seasonal framework.**

Abstract
We study the infestation dynamics of banana or plantain plants by Radopholus similis, a plant-parasitic nematode that causes severe damages. Two control strategies are implemented in our model: pesticides, which are widely used, and fallows, which are more environmentally friendly. To represent the host-parasite dynamics, two semi-discrete models are proposed. During each cropping season, free nematodes enter the plant roots, on which they feed and reproduce. At the end of the cropping season, fruits are harvested. In the first model, the parent plant is cut down to be replaced by one of its suckers and p...

**Source: **Mathematical Biosciences - February 21, 2020 **Category: **Statistics **Authors: **Tankam-Chedjou I, Touzeau S, Mailleret L, Tewa JJ, Grognard F **Tags: **Math Biosci **Source Type: **research

**Stochastic dynamics in a time-delayed model for autoimmunity.**

Abstract
In this paper we study interactions between stochasticity and time delays in the dynamics of immune response to viral infections, with particular interest in the onset and development of autoimmune response. Starting with a deterministic time-delayed model of immune response to infection, which includes cytokines and T cells with different activation thresholds, we derive an exact delayed chemical master equation for the probability density. We use system size expansion and linear noise approximation to explore how variance and coherence of stochastic oscillations depend on parameters, and to show that st...

**Source: **Mathematical Biosciences - February 21, 2020 **Category: **Statistics **Authors: **Fatehi F, Kyrychko YN, Blyuss KB **Tags: **Math Biosci **Source Type: **research

**Investigation into the role of macrophages heterogeneity on solid tumour aggregations.**

Abstract
Macrophages are one of the most important immune cell populations that can be found inside solid tumours. For a long time, it was thought that these cells have an anti-tumour role, but relatively recent research has shown that they can have both anti-tumour and pro-tumour roles as determined by their phenotypes. Due to the heterogeneity and plasticity of macrophage population, with cells changing their phenotypes in response to the tumour microenvironment, it is difficult to fully understand their role inside the solid tumours. Here we consider a mathematical modelling and computational approach to invest...

**Source: **Mathematical Biosciences - February 20, 2020 **Category: **Statistics **Authors: **Eftimie R **Tags: **Math Biosci **Source Type: **research

**About biomass overyielding of mixed cultures in batch processes.**

Abstract
We study mechanisms that can produce an increase of biomass production in batch processes when considering mixed cultures, compared to pure cultures. We show that growth thresholds or variable yields can produce 'overyielding', while this is not possible in the classical batch model with multiple species. We give sufficient conditions on the characteristics of the species to obtain overyielding, and illustrate these theoretical results with numerical simulations. This work provides new insights on species complementary in models of mixed cultures, without having to consider direct interactions terms betwe...

**Source: **Mathematical Biosciences - February 11, 2020 **Category: **Statistics **Authors: **Rapaport A, Nidelet T, El Aida S, Harmand J **Tags: **Math Biosci **Source Type: **research

**Reducing a model of sugar metabolism in peach to catch different patterns among genotypes.**

zzi V
Abstract
Several studies have been conducted to understand the dynamic of primary metabolisms in fruit by translating them into mathematics models. An ODE kinetic model of sugar metabolism has been developed by Desnoues et al. [1] to simulate the accumulation of different sugars during peach fruit development. Two major drawbacks of this model are (a) the number of parameters to calibrate and (b) its integration time that can be long due to non-linearity and time-dependent input functions. Together, these issues hamper the use of the model for a large panel of genotypes, for which few data are available...

**Source: **Mathematical Biosciences - January 31, 2020 **Category: **Statistics **Authors: **Kanso H, Quilot-Turion B, Memah MM, Bernard O, Gouzé JL, Baldazzi V **Tags: **Math Biosci **Source Type: **research

**Exact and approximate formulas for contact tracing on random trees.**

r J
Abstract
We consider a stochastic susceptible-infected-recovered (SIR) model with contact tracing on random trees and on the configuration model. On a rooted tree, where initially all individuals are susceptible apart from the root which is infected, we are able to find exact formulas for the distribution of the infectious period. Thereto, we show how to extend the existing theory for contact tracing in homogeneously mixing populations to trees. Based on these formulas, we discuss the influence of randomness in the tree and the basic reproduction number. We find the well known results for the homogeneously mix...

**Source: **Mathematical Biosciences - January 31, 2020 **Category: **Statistics **Authors: **Okolie A, Müller J **Tags: **Math Biosci **Source Type: **research

**Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models.**

Abstract
The phenomenon of chondrogenic pattern formation in the vertebrate limb is one of the best studied examples of organogenesis. Many different models, mathematical as well as conceptual, have been proposed for it in the last fifty years or so. In this review, we give a brief overview of the fundamental biological background, then describe in detail several models which aim to describe qualitatively and quantitatively the corresponding biological phenomena. We concentrate on several new models that have been proposed in recent years, taking into account recent experimental progress. The major mathematical to...

**Source: **Mathematical Biosciences - January 27, 2020 **Category: **Statistics **Authors: **Chatterjee P, Glimm T, Kaźmierczak B **Tags: **Math Biosci **Source Type: **research

**On the role of the epithelium in a model of sodium exchange in renal tubules.**

In this study we present a mathematical model describing the transport of sodium in a fluid circulating in a counter-current tubular architecture, which constitutes a simplified model of Henle's loop in a kidney nephron. The model explicitly takes into account the epithelial layer at the interface between the tubular lumen and the surrounding interstitium. In a specific range of parameters, we show that explicitly accounting for transport across the apical and basolateral membranes of epithelial cells, instead of assuming a single barrier, affects the axial concentration gradient, an essential determinant of the urinary co...

**Source: **Mathematical Biosciences - January 21, 2020 **Category: **Statistics **Authors: **Marulli M, Edwards A, Milišić V, Vauchelet N **Tags: **Math Biosci **Source Type: **research

**Sensitivity analysis methods in the biomedical sciences.**

Abstract
Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before applying each method to a simple model. Also included is a summary of current software packages, as well as a modeller's guide for carrying out sensitivity analyses. Finally, we apply the popular Morris and Sobol methods to two models with biomedical applications, with the intention of providing a deeper understanding behind both the principles of these methods and the presen...

**Source: **Mathematical Biosciences - January 14, 2020 **Category: **Statistics **Authors: **Qian G, Mahdi A **Tags: **Math Biosci **Source Type: **research

**Multiscale Moving Boundary Modelling of Cancer Interactions with a Fusogenic Oncolytic Virus: the Impact of Syncytia Dynamics.**

Abstract
Oncolytic viral therapies is one of the new promising strategies against cancer, due to the ability of oncolytic viruses to specifically replicate inside cancer cells and kill them. There is increasing evidence that a sub-class of viruses that contain fusion proteins (triggering the formation of syncytia) can lead to better oncolytic results. Since the details of the tumour dynamics following syncytia formation are not fully understood, in this study we consider a modelling and computational approach to describe the effect of a fusogenic oncolytic virus on the multiscale dynamics of a spreading tumour. We...

**Source: **Mathematical Biosciences - December 27, 2019 **Category: **Statistics **Authors: **Alzahrani T, Eftimie R, Trucu D **Tags: **Math Biosci **Source Type: **research

**Assessing the role of human mobility on malaria transmission.**

Abstract
South Sudan accounts for a large proportion of all annual malaria cases in Africa. In recent years, the country has witnessed an unprecedented number of people on the move, refugees, internally displaced people, people who have returned to their countries or areas of origin, stateless people and other populations of concern, posing challenges to malaria control. Thus, one can claim that human mobility is one of the contributing factors to the resurgence of malaria. The aim of this paper is to assess the impact of human mobility on the burden of malaria disease in South Sudan. For this, we formulate an SIR...

**Source: **Mathematical Biosciences - December 26, 2019 **Category: **Statistics **Authors: **Mukhtar AYA, Munyakazi JB, Ouifki R **Tags: **Math Biosci **Source Type: **research

**Risk Structured Model of Cholera Infections in Cameroon.**

Abstract
Since 1991, Cameroon, a cholera endemic African country, has been experiencing large cholera outbreaks and cholera related deaths. In this paper, we use a "fitted" demographic equation (disease-free equation) to capture the total population of Cameroon, and then use a fitted low-high risk structured cholera differential equation model to study reported cholera cases in Cameroon from 1987-2004. For simplicity, our model has no spatial structure. The basic reproduction number of our fitted cholera model, R0, is bigger than 1 and our model predicted cholera endemicity in Cameroon. In addition, the ...

**Source: **Mathematical Biosciences - December 16, 2019 **Category: **Statistics **Authors: **Che EN, Kang Y, Yakubu AA **Tags: **Math Biosci **Source Type: **research

**The application of machine learning to disease diagnosis and treatment.**

PMID: 31857093 [PubMed - as supplied by publisher] (Source: Mathematical Biosciences)

**Source: **Mathematical Biosciences - December 16, 2019 **Category: **Statistics **Authors: **Zou Q, Ma Q **Tags: **Math Biosci **Source Type: **research

**Addition of flow reactions preserving multistationarity and bistability.**

Abstract
We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows and outflows, while in fact some of the species might be degraded or leaked to the environment, or be synthesized or transported into the system. We provide a sufficient and easy-to-check criterion based on the stoichiometry of the reaction network alone and discuss examples from systems biology.
PMID: 31843554 [PubMed - as supplied by publisher] (Source: Mathematical Biosciences)

**Source: **Mathematical Biosciences - December 13, 2019 **Category: **Statistics **Authors: **Cappelletti D, Feliu E, Wiuf C **Tags: **Math Biosci **Source Type: **research

**The Basic Reproductive Number for Disease Systems with Multiple Coupled Heterogeneities.**

Abstract
In mathematical epidemiology, a well-known formula describes the impact of heterogeneity on the basic reproductive number, R0, for situations in which transmission is separable and for which there is one source of variation in susceptibility and one source of variation in infectiousness. This formula is written in terms of the magnitudes of the heterogeneities, as quantified by their coefficients of variation, and the correlation between them. A natural question to ask is whether analogous results apply when there are multiple sources of variation in susceptibility and/or infectiousness. In this paper we ...

**Source: **Mathematical Biosciences - December 10, 2019 **Category: **Statistics **Authors: **Lloyd AL, Kitron U, Perkins TA, Vazquez-Prokopec GM, Waller LA **Tags: **Math Biosci **Source Type: **research