Interaction Between Mosquito Population Dynamics And Malaria Dynamics

Nowadays,malaria is still one of the most serious threats to public health,causing hundreds of millions of cases and hundreds of thousands of deaths every year.Malaria is a mosquito-borne disease caused by Plasmodium parasites,which are transmitted to humans through the bites of female Anopheles mosquitoes.Infection with Plasmodium parasites not only harms humans,but also affects the fecundity,life span and biting be-havior of mosquitoes.Based on the classical Ross-Macdonald model,we establish a malaria model with the consideration of disease-induced deaths in humans and adverse effects on mosquitoes.The basic reproduction number of the model,R₀,is defined and it is shown that the model can exhibit backward bifurcation atR₀=1.Secondly,we analyze the special case where the disease-induced mortality in humans is ignored,and prove that the disease-free equilibrium is globally asymptotically stable asR₀≤1.Sufficient condition for the local asymptotic stability of the endemic equilibrium is given provided thatR₀>1.Finally,we use numerical simulation to further explore the impact of infection on infectious disease dynamics and mosquito population dynamics.