LAUSR

In this paper effect of insecticides has been studied for the control of vector-borne diseases, like malaria. A nonlinear SIS mathematical model has been proposed and analyzed for transmission of malaria caused by infected mosquito population on susceptible human population using chemicals to control the disease. It is further assumed that susceptible human population becomes infected by direct contact with vector mosquitoes. The mosquito population density is assumed to be governed by general logistic model. It is found that model exhibits three nonnegative equilibria, namely mosquito and disease-free equilibrium $$E_{0} ,$$ E 0 , mosquito persistence and disease-free equilibrium $$E_{1}$$ E 1 and endemic equilibrium $$E^{*}$$ E ∗ . The model is analyzed by using local and global stability theory of differential equations and numerical simulation.