Stochastic Stability and Analytical Solution with Homotopy Perturbation Method of Multicompartment Non-Linear Epidemic Model with Saturated Rate

Laid Chahrazed
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Laid Chahrazed: Department of Mathematics, Faculty of Exact Sciences, University Freres Mentouri, Constantine 1, Algeria

Academic Journal of Applied Mathematical Sciences, 2021, vol. 7, issue 3, 149-157

Abstract: In this work, we consider a nonlinear epidemic model with a saturated incidence rate. we consider a population of size N(t) at time t, this population is divided into six subclasses, with N(t)=S(t)+I(t)+I?(t)+I?(t)+I?(t)+Q(t). Where S(t), I(t), I?(t), I?(t), I?(t), and Q(t) denote the sizes of the population susceptible to disease, infectious members, and quarantine members, respectively. We have made the following contributions: 1. The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determined by the ratio called the basic reproductive number. 2. We find the analytical solution of the nonlinear epidemic model by Homotopy perturbation method. 3. Finally the stochastic stabilities. The study of its sections are justified with theorems and demonstrations under certain conditions. In this work, we have used the different references cited in different studies in the three sections already mentioned.

Keywords: : Homotopy perturbation method; Incidence rate; Local stability; Nonlinear epidemic model; Stochastic stability. (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:arp:ajoams:2021:p:149-157

DOI: 10.32861/ajams.73.149.157

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