Malaria Transmission and Biological Control with Human Related Activities: A Mathematical Modeling Approach

Abstract

In this paper, a nonlinear mathematical model for the control of vector borne diseases, like malaria is proposed and analyzed. In the
modeling process it is assumed that the mosquito population is controlled by using Larvivorous fish, which partially depends on the
larva of mosquito population. It is further assumed that the mosquito population grows logistically in the environment and its intrinsic growth rate is also affected by the human related activities. The equilibria of the model are obtained and their stability is discussed by using stability theory of differential equations. The threshold for the eradication of the disease, i.e. basic reproduction number is obtained. The analysis of the model shows that the growth rate in mosquito population due to human related activities has destabilizing effect on the system. Further numerical simulation is performed to verify the analytically obtained results.