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arXiv · 1905.04920

Mathematical analysis of complex SIR model with coinfection and density dependence

Samia Ghersheen·Vladimir Kozlov·Vladimir G. Tkachev·Uno Wennergren
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Abstract

An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed and several threshold conditions are obtained which describes the establishment of disease in the population. We prove that for small carrying capacity $K$ there exist a globally stable disease free equilibrium point. Furthermore, we establish the continuity of the transition dynamics of the stable equilibrium point, i.e. we prove that (1) for small values of $K$ there exists a unique globally stable equilibrium point, and (b) it moves continuously as $K$ is growing (while its face type may change). This indicate that carrying capacity is the crucial parameter and increase in resources in terms of carrying capacity promotes the risk of infection.

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Samia Ghersheen, Vladimir Kozlov, Vladimir G. Tkachev, Uno Wennergren. 2019-05-13. Mathematical analysis of complex SIR model with coinfection and density dependence. https://doi.org/10.1002/cmm4.1042

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