Mathematical modeling of combined therapies for treating tumor drug resistance
Math Biosci. 2024 Mar 11;371:109170. doi: 10.1016/j.mbs.2024.109170. Online ahead of print.ABSTRACTDrug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carr...
Source: Mathematical Biosciences - March 11, 2024 Category: Statistics Authors: Kangbo Bao Guizhen Liang Tianhai Tian Xinan Zhang Source Type: research
Mathematical modeling of combined therapies for treating tumor drug resistance
Math Biosci. 2024 Mar 11;371:109170. doi: 10.1016/j.mbs.2024.109170. Online ahead of print.ABSTRACTDrug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carr...
Source: Mathematical Biosciences - March 11, 2024 Category: Statistics Authors: Kangbo Bao Guizhen Liang Tianhai Tian Xinan Zhang Source Type: research
Mathematical modeling of combined therapies for treating tumor drug resistance
Math Biosci. 2024 Mar 9:109170. doi: 10.1016/j.mbs.2024.109170. Online ahead of print.ABSTRACTDrug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carried o...
Source: Mathematical Biosciences - March 11, 2024 Category: Statistics Authors: Kangbo Bao Guizhen Liang Tianhai Tian Xinan Zhang Source Type: research
Mathematical modeling of combined therapies for treating tumor drug resistance
Math Biosci. 2024 Mar 9:109170. doi: 10.1016/j.mbs.2024.109170. Online ahead of print.ABSTRACTDrug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carried o...
Source: Mathematical Biosciences - March 11, 2024 Category: Statistics Authors: Kangbo Bao Guizhen Liang Tianhai Tian Xinan Zhang Source Type: research
Structural instability and linear allocation control in generalized models of substance use disorder
Math Biosci. 2024 Mar 2;371:109169. doi: 10.1016/j.mbs.2024.109169. Online ahead of print.ABSTRACTSubstance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, includ...
Source: Mathematical Biosciences - March 4, 2024 Category: Statistics Authors: Leigh B Pearcy Suzanne Lenhart W Christopher Strickland Source Type: research
Structural instability and linear allocation control in generalized models of substance use disorder
Math Biosci. 2024 Mar 2;371:109169. doi: 10.1016/j.mbs.2024.109169. Online ahead of print.ABSTRACTSubstance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, includ...
Source: Mathematical Biosciences - March 4, 2024 Category: Statistics Authors: Leigh B Pearcy Suzanne Lenhart W Christopher Strickland Source Type: research
Structural instability and linear allocation control in generalized models of substance use disorder
Math Biosci. 2024 Mar 2;371:109169. doi: 10.1016/j.mbs.2024.109169. Online ahead of print.ABSTRACTSubstance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, includ...
Source: Mathematical Biosciences - March 4, 2024 Category: Statistics Authors: Leigh B Pearcy Suzanne Lenhart W Christopher Strickland Source Type: research
Structural instability and linear allocation control in generalized models of substance use disorder
Math Biosci. 2024 Mar 2;371:109169. doi: 10.1016/j.mbs.2024.109169. Online ahead of print.ABSTRACTSubstance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, includ...
Source: Mathematical Biosciences - March 4, 2024 Category: Statistics Authors: Leigh B Pearcy Suzanne Lenhart W Christopher Strickland Source Type: research
Structural instability and linear allocation control in generalized models of substance use disorder
Math Biosci. 2024 Mar 2;371:109169. doi: 10.1016/j.mbs.2024.109169. Online ahead of print.ABSTRACTSubstance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, includ...
Source: Mathematical Biosciences - March 4, 2024 Category: Statistics Authors: Leigh B Pearcy Suzanne Lenhart W Christopher Strickland Source Type: research
Structural instability and linear allocation control in generalized models of substance use disorder
Math Biosci. 2024 Mar 2:109169. doi: 10.1016/j.mbs.2024.109169. Online ahead of print.ABSTRACTSubstance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, including ...
Source: Mathematical Biosciences - March 4, 2024 Category: Statistics Authors: Leigh B Pearcy Suzanne Lenhart W Christopher Strickland Source Type: research
Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics
Math Biosci. 2024 Feb 24;370:109168. doi: 10.1016/j.mbs.2024.109168. Online ahead of print.ABSTRACTWe here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states. We then describe the spatio-temporal evolution of the concentration of oxygen and of tumor-secreted proteolytic enzymes using partial differenti...
Source: Mathematical Biosciences - February 26, 2024 Category: Statistics Authors: Marco Scianna Source Type: research
Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics
Math Biosci. 2024 Feb 24;370:109168. doi: 10.1016/j.mbs.2024.109168. Online ahead of print.ABSTRACTWe here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states. We then describe the spatio-temporal evolution of the concentration of oxygen and of tumor-secreted proteolytic enzymes using partial differenti...
Source: Mathematical Biosciences - February 26, 2024 Category: Statistics Authors: Marco Scianna Source Type: research
Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics
Math Biosci. 2024 Feb 24;370:109168. doi: 10.1016/j.mbs.2024.109168. Online ahead of print.ABSTRACTWe here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states. We then describe the spatio-temporal evolution of the concentration of oxygen and of tumor-secreted proteolytic enzymes using partial differenti...
Source: Mathematical Biosciences - February 26, 2024 Category: Statistics Authors: Marco Scianna Source Type: research
Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics
Math Biosci. 2024 Feb 24;370:109168. doi: 10.1016/j.mbs.2024.109168. Online ahead of print.ABSTRACTWe here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states. We then describe the spatio-temporal evolution of the concentration of oxygen and of tumor-secreted proteolytic enzymes using partial differenti...
Source: Mathematical Biosciences - February 26, 2024 Category: Statistics Authors: Marco Scianna Source Type: research
Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics
Math Biosci. 2024 Feb 24:109168. doi: 10.1016/j.mbs.2024.109168. Online ahead of print.ABSTRACTWe here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states. We then describe the spatio-temporal evolution of the concentration of oxygen and of tumor-secreted proteolytic enzymes using partial differential e...
Source: Mathematical Biosciences - February 26, 2024 Category: Statistics Authors: Marco Scianna Source Type: research
