Impact of the diffusion coefficient and non-linear incidence rate on the dynamics of the SIR model

This paper proposes a susceptible-infected-–infected–recovered SIR- mathematical model with diffusion coefficient. Nonlinear incidence and treatment rates are employed to control infectious diseases and epidemics. For the study, the treatment rate is regarded as Holling type $II$ function, while the infection incidence rate is viewed as Crowley–Martin type function. A detailed mathematical analysis is carried out that includes non-negativity and existence of solution, existence of both type disease free and endemic equilibrium points. Further, stability analysis at equilibrium points is performed. Additionally, the numerical simulation is conducted and graphical representations are displayed. The results show the impact of diffusion coefficients and non-linear incident and recovery rate on susceptible, infected and recovered populations.