Modeling the effects of media information and saturated treatment on malaria disease with NSFD method

Whenever a disease spreads in the population, people have a tendency to alter their behavior due to the availability of knowledge concerning disease prevalence. Therefore, the incidence term of the model must be suitably changed to reflect the impact of information. Furthermore, a lack of medical resources affects the dynamics of disease. In this paper, a mathematical model of malaria of type $S_h{I}_h{R}_h-S_v{I}_v$ with media information and saturated treatment is considered. The analysis of the model is performed and it is established that when the basic reproduction number, ${{ℛ}}_0$, is less than unity, the disease may or may not die out due to saturated treatment. Furthermore, it is pointed out that if medical resources are accessible to everyone, disease elimination in this situation is achievable. The global asymptotic stability of the unique endemic equilibrium point (EEP) is established using the geometric approach under parametric restriction. The sensitivity analysis is also carried out using the normalized forward sensitivity index (NFSI). It is difficult to derive the analytical solution for the governing model due to it being a system of highly nonlinear ordinary differential equations. To overcome this challenge, a specialized numerical scheme known as the non-standard finite difference (NSFD) approach has been applied. The suggested numerical method is subjected to an elaborate theoretical analysis and it is determined that the NSFD scheme maintains the positivity and conservation principles of the solutions. It is also established that the disease-free equilibrium (DFE) point has the same local stability criteria as that of continuous model. Our proposed NSFD scheme also captures the backward bifurcation phenomena. The outcomes of the NSFD scheme are compared to two well-known standard numerical techniques, namely the fourth-order Runge–Kutta (RK4) method and the forward Euler method.