Analysis of SEIR model for two target population with optimal control and stochastic approach

Abstract The present study introduces a SEIR (Susceptible-Exposed-Infected-Recovered) model that incorporates the individual awareness regarding the disease transmission. Based on this understanding, the susceptible population is divided into two distinct classes: aware and unaware. It is assumed that there is unrestricted interaction between these two susceptible populations. The model demonstrates two distinct steady states: disease-free steady (DFS) and endemic steady (ES) state. Additionally, conditions for the stability of both steady states are derived. The results indicate that the DFS state is stable when the basic reproduction number (BRN) is less than unity, whereas the ES state exists when BRN is greater than unity and is locally stable under specific parametric conditions. Furthermore, the system is numerically solved using Matlab . Results indicate that unaware individuals are at a higher risk of infection compared to those who are aware. The impact of specific parameters on the population dynamics are shown graphically. Additionally, optimal control study is performed to regulate the infection in the population. Various control strategies have been considered and the most effective strategy to curb the spread of infection involves reducing the number of susceptibles, exposed and infected individuals while increasing the recovered individuals. Furthermore, the proposed model is modified to a stochastic differential equation (SDE) model by adding noise to each equation involving the state variables. This study aims to observe the population dynamics under the influence of additive noise. It is concluded that high noise intensity causes population fluctuations, leading to unstable nature of the system.