ArticleTheory in biosciences = Theorie in den Biowissenschaften2020
A study on the stability behavior of an epidemic model with ratio-dependent incidence and saturated treatment.
Article in Theory in biosciences = Theorie in den Biowissenschaften, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
In the present article, the dynamics of a novel combination of ratio-dependent incidence rate and saturated treatment rate in susceptible-infected-recovered disease compartmental model has been presented. The ratio-dependent incidence rate has been incorporated into the model to monitor the situation when ratio of the number of infectives to that of the susceptibles is getting higher. The saturated treatment rate of the infected population has been considered as Holling type II functional, which explains the limitation in treatment availability. From the mathematical analysis of the model, two types of equilibria of the model have been obtained, which are named as disease-free equilibrium (DFE) and endemic equilibrium (EE). The local stability behavior of equilibria has been investigated by the basic reproduction number [Formula: see text], center manifold theory and Routh-Hurwitz criterion. It has been investigated that the DFE is locally asymptotically stable when [Formula: see text], and when [Formula: see text], the DFE exhibits either a forward bifurcation or a backward bifurcation under some conditions. The local stability behavior of the EE has also been analyzed, and some conditions are obtained for the same. Finally, some numerical computations have been performed in support of our theoretical results.
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