Stability of the equilibria in a discrete-time sivs epidemic model with standard incidence | Zendy

Mahmood Parsamanesh | Zendy; S. Mehrshad | Zendy

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Stability of the equilibria in a discrete-time sivs epidemic model with standard incidence

Author(s) -

Mahmood Parsamanesh,

S. Mehrshad

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1908393p

Subject(s) - mathematics , bifurcation , stability (learning theory) , epidemic model , basic reproduction number , bifurcation diagram , discrete time and continuous time , transcritical bifurcation , lyapunov function , lyapunov exponent , population , statistics , demography , nonlinear system , physics , quantum mechanics , machine learning , sociology , computer science

A discrete-time SIS epidemic model with vaccination is presented and studied. The model includes deaths due to disease and the total population size is variable. First, existence and positivity of the solutions are discussed and equilibria of the model and basic reproduction number are obtained. Next, the stability of the equilibria is studied and conditions of stability are obtained in terms of the basic reproduction number R0. Also, occurrence of the fold bifurcation, the flip bifurcation, and the NeimarkSacker bifurcation is investigated at equilibria. In addition, obtained results are numerically discussed and some diagrams for bifurcations, Lyapunov exponents, and solutions of the model are presented.

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