Mathematical Model of Typhoid Disease Using Standard and Non-standard Finite Difference Schemes

Abstract In the current paper, typhoid disease is mathematically simulated, and its positivity and boundedness are also discussed. The fundamental reproduction number \({R}_{0}\), which is significant in epidemiology, is sorted out. The Lyapunov function for global stability and the Routh-Hurwitz criterion for local stability of the intended NSFD scheme are studied for disease-free and endemic equilibrium points, respectively. The standard finite difference (SFD) scheme and non-standard finite difference (NSFD) scheme are used to approximate the solution of the PSEIT epidemic model.