Modeling the Dynamics of Malaria in a Random Environment

Malaria is still ranked among one of the world’s top killers. According to WHO report released in December 2016, there were 212 million cases of malaria resulting in about 429 thousand deaths. Moreover, more than two thirds of the global malaria related deaths are children under the age of 5. In this study a family of models is presented to study malaria in a stochastic and deterministic setting. The family type is determined by the qualitative behavior of the nonlinear incidence rates of the disease. The more realistic stochastic setting includes the random environmental fluctuations in the disease transmission and natural death rates of humans which are represented by independent white noise processes. The family of malaria models exhibits three random delays: - two of the delays represent the incubation periods of the malaria plasmodium inside the vector and human hosts, whereas the third delay is the period of effective natural immunity against the disease. Insights about the effects of the delays and the noises on the malaria dynamics are gained via comparative analyses of the family of stochastic and deterministic models. The results of the study are of great significance to (1) disease eradication and extinction, and to (2) persistence and permanence of the disease in the human population. Numerical simulation results are presented