Investigation of SIR Model with two Susceptible Classes

The present work presents a dual compartmental SIR model which takes into account the awareness of the disease among the population. Based on this understanding, the susceptible population is divided into two distinct classes, aware and unaware class. The primary assumption is that there is a free interaction between these two susceptible populations. The system exhibits two distinct equilibrium states. The basic reproduction number is calculated utilizing the next generation matrix (NGM) approach. Further, conditions for the stability of both the equilibrium states are derived. Numerical simulation is employed to solve the system and the findings are presented through graphs. Results show that the individuals with no awareness are infected at a higher rate than the aware individuals. Furthermore, the impact of certain parameters of interest are shown graphically. In conclusion, it can be inferred that being aware is a crucial element in minimizing the outbreak of infectious disease in the society, in general.