Mathematical analysis and optimal control of a cholera epidemic in different human communities with individuals’ migration

Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Eric Kokomo, Bongor Danhrée, Yves EmvuduAbstractWe propound a deterministic, nonlinear model for the transmission dynamics of cholera in different human communities with individuals’ migration. The considered different human communities are crossed by a running water which is contaminated by the vibrio cholerae bacterium. The formulated model for each community which is an initial/boundary-value problem constituted of four parabolic partial differential equations, integrates antibiotic treatment, hydration therapy and contaminated water treatment as control mechanisms of the disease. Using semigroup theory, we prove that this model has a unique bounded positive solution. Also under a given condition, the existence of a trivial equilibrium and of a nontrivial equilibrium of each community is established and their local and global stabilities are studied. In analysis of Turing’s instability, we determine sufficient conditions allowing the formation of a spatially stationary and periodic heterogeneous pattern. Analytically the existence of a unique optimal control is established by the use of functional analysis techniques and an optimal control θ̄ is determined to eradicate the epidemic in each community. In order to confirm our theoretical results, we finish with a real-world application concerning the cholera epidemic that took place in Cameroon in 2...
Source: Nonlinear Analysis: Real World Applications - Category: Research Source Type: research

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Source: TIME: Health - Category: Consumer Health News Authors: Tags: Uncategorized 2019-nCoV Infectious Disease Source Type: news
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Source: Infection, Genetics and Evolution - Category: Genetics & Stem Cells Authors: Tags: Infect Genet Evol Source Type: research
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Source: Journal of Preventive Medicine and Hygiene - Category: International Medicine & Public Health Source Type: research
The burden of diarrheal diseases is very high, accounting for 1.7 to 5 billion cases per year worldwide. Typhoid Fever (TF) and Cholerare potentially life-threatening infectious diseases mainly transmitted through the consumption of food, drink or water that have been contaminated by the feces or urine of subjects excreting the pathogen. TF is mainly caused by Salmonella typhi whereas Cholera is caused by intestinal infection by the toxin-producing bacterium Vibrio cholerae. These diseases typically affect low- and middle-income countries where housing is overcrowded and wa...
Source: Journal of Preventive Medicine and Hygiene - Category: International Medicine & Public Health Source Type: research
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