Modeling and Analysis of an Imprecise Epidemic System with Optimal Treatment and Vaccination Control

Abstract

In this paper, we propose and analyze a Susceptible-Vaccinated-Exposed-Infected-Recovered (SVEIR) type infectious disease model with imprecise parameters. Introducing the interval numbers in functional form, the SVEIR model is proposed and formulated. The existence of possible equilibrium points with their feasibility criteria and an explicit value of basic reproduction number is obtained. The asymptotic stability of the system at different equilibrium points are also discussed. Next by considering treatment and vaccination as two control parameters, an optimal control problem is formulated and solved. Finally, some computer simulation works are given in support of our analytical results.

An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness

“…Zadeh ( 1965 ) first introduced fuzzy set theory to study the uncertainty in mathematics. Das and Pal ( 2018 ) proposed the imprecise epidemic system with optimal treatment and vaccination to control the epidemic. Researchers paid attention to develop the epidemic models in uncertain environments (Pontryagin et al 1962 ; Panja et al 2017 ; Mahata et al 2018 ; Nandi et al 2018 ; Das et al 2020a ).…”