Fuzzy Analysis of SVIRS Disease System with Holling Type-II Saturated Incidence Rate and Saturated Treatment

Abstract

This article presents a fuzzy SVIRS disease system with Holling type-II saturated incidence rate and saturated treatment, in which all parameters related to population dynamics have been considered as fuzzy numbers. Then, the existence condition and permanence of the SVIRS model have been discussed and we derived disease-free and endemic equilibrium points of the proposed fuzzy system. The local stability conditions of the fuzzy system around these equilibrium points using Routh–Hurwitz criteria are discussed. We also verified global stability around the interior steady state using Lozinskii measure. Computer simulations are provided to understand the dynamics of the proposed system. Parameter analysis is carried out with the help of computer simulation. Fuzzy provides better solution for any disease modeling in many ways like disease detection and transmission, different stages of disease, risk analysis (through parameter analysis), and optimal recovery solutions. Earlier literature acts as background to startup this disease modeling and optimal solutions provided by fuzzy logic is one of the motivational key element behind this fuzzy SVIRS model with Holling type-II and its analysis by both analytical and computer simulation.