Plasmodium vivax, Plasmodium falciparum, Plasmodium ovale and Plasmodium malariae causing human malaria. The difference between P.vivax malaria and P. falciparum malaria is that a person suffering from P. vivax

Malaria is an infectious disease caused by the bite of female Anopheles mosquitoes. There are four species, namely, Plasmodium vivax, Plasmodium falciparum, Plasmodium ovale and Plasmodium malariae causing human malaria. The difference between P.vivax malaria and P. falciparum malaria is that a person suffering from P. vivax infection can suffer relapses of the disease. The effect of a time delay on the transmission of this disease is studied. The time delay is the period in which the P.vivax parasite develops inside the mosquito (vector) before the vector becomes infectious (i.e., pass on the infection). The model is analyzed by using standard dynamic modeling method. Two stable equilibrium states are found to be possible. It is found that the disease free equilibrium state is stable when a newly defined basic reproduction number L is less than one. If L is greater than one, the endemic equilibrium state is stable. The conditions for the endemic equilibrium state to be a stable spiral node are found. For realistic values of the parameters in the model, it is found that solutions in phase space are trajectories spiraling into the endemic equilibrium state. The bifurcation diagrams of our model are discussed. It is shown that the limit cycle and chaotic behaviors can occur with only unrealistic situations. Keywords—Limit cycle, local stability, Plasmodium Vivax, time delay.