Mathematical Modeling of Malaria with Saturated Treatment-A Case Study of India

Malaria is a life-threatening mosquito-borne disease. It is transmitted through the bite of an infected Anopheles mosquito. People who get infected with malaria become very sick with high fevers, chills, and flu-like symptoms. Malaria may be fatal if not treated promptly. Here we propose an SIS model to study the trans- mission dynamics of malaria with saturated treatment. We assume that the mosquito population is growing logistically in the environment. Here we include a saturated type treatment function which is more suitable for the regions with limited resources. We discuss the existence and stability of different equilibria of the proposed model. We also compute the basic reproduction number R0 which plays an important role in existence and stability of equilibria of the model. We estimate the parameter corresponding to transmission of malaria using real data from different states of India by least square method. We also perform sensitivity analysis using PRCC to identify the key parameters which influence the basic reproduction number and system both, hence regulate the transmission dynamics of malaria. Numerical simulations are presented to illustrate the analytic findings.