Fuzzy SEIR Modeling and Analysis of COVID-19 Spread and Control

Abstract

The main objective of the paper is to construct an susceptible-exposed-infected-recovered (SEIR) mathematical model by considering the transmission rate, death rate, and recovery rate as fuzzy parameters since we assumed heterogeneity in the population. We have examined the domain of the solutions and discussed the uniqueness of the constructed SEIR model. A qualitative analysis has been carried out to determine the stability of COVID-19 using Routh-Hurwitz criteria. The basic reproduction number is obtained using the next-generation matrix method. Fuzzy basic reproduction numbers with respect to various virus loads have been calculated to know how fast the disease spreads at different levels of virus loads. One of the main aims is to perform sensitivity analysis, which is essential for determining the controlling parameter and helps the government and other policymakers develop regulations for the prevention and control of the spread. The numerical simulation, which has been calculated using the homotopy perturbation method and illustrated graphically, shows the importance of getting vaccinated, which is important in controlling the spread of COVID-19.