Mathematical Model of Malaria for Co-infection of Plasmodium vivax and Plasmodium falciparum in India

Abstract

Malaria is caused by the protozoan parasites of genus Plasmodium. Plasmodium falciparum is the most common cause of malaria in Africa and South-East Asia. In India, Plasmodium vivax has been the primary pathogen responsible for malaria, even though Plasmodium falciparum cases are on the rise in recent times. We develop a mathematical model ShE1E2E3I1I2I3RSh of malaria in human population with vertical transmission for Plasmodium vivax, Plasmodium falciparum and co-infection of both Plasmodium vivax and Plasmodium falciparum parasites and SmEmIm model in mosquito population. The stability of the system under different conditions for disease–free equilibrium and endemic equilibrium are established. Extensive numerical simulations are carried out to establish the analytical results with real parametric values and sensitivity analysis of basic reproduction number is also carried out with the transmission probability for malaria in human population. Finally, we compare all three infected classes of Plasmodium vivax, Plasmodium falciparum and co-infection of both the parasites with real value parameters by numerical simulation and also calculated its basic reproduction numbers.