Dynamics of an $${ SVEIRS}$$ SVEIRS Epidemic Model with Vaccination and Saturated Incidence Rate

Abstract

Measles and influenza are two major diseases-caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immunity and saturation incidence rate. The dissection of the proposed model is conferred in terms of the associated reproduction number R v , which is determined by the next-generation approach and obtained that if R v ≤ 1, the diseasefree equilibrium exists and it is locally as well as globally asymptotically stable. Further for R v > 1, a unique endemic equilibrium exists and it is also locally as well as globally asymptotically stable under certain conditions, which shows the prevalence and persistence of the disease in the population.

Qualitative and Quantitative Analyses of COVID-19 Dynamics

“…Further, we establish the global asymptotic stability of the endemic equilibrium solution by proving that solution trajectories converge to the endemic equilibrium point for R 0 > 1. We shall carry this out by constructing a suitable Lyapunov candidate function of Goh-Volterra type (see [28,29] and the references cited therein). The result below establishes the global stability of the endemic equilibrium solution E 1 .…”