A periodic malaria model with two delays

Malaria is the world's most prevalent mosquito-borne disease caused by Plasmodium parasites, and responsible for over half a million deaths per year. To understand the effects of the intrinsic and extrinsic incubation periods of the parasite within the humans and mosquitoes, respectively, and the seasonality on disease transmission, we propose a periodic malaria model with delays. The basic reproduction number no is derived, and it is shown that R-0 is a threshold parameter between the extinction and persistence of the disease. In the case where all the coefficients are constants and the intrinsic incubation period is ignored, we also prove the global attractivity of the endemic equilibrium when R-0 > 1. Numerical simulations indicate that prolonging the incubation period in mosquitoes is more effective than prolonging the incubation period in humans for disease control. It is also found that increasing the strength of seasonal forcing will lead to a higher epidemic peak. (C) 2019 Elsevier B.V. All rights reserved.