A climate-based malaria model with the use of bed nets
Insecticide-treated bed nets (ITNs) are among the most important and effective intervention measures against malaria. In order to investigate the impact of bed net use on disease control, we formulate a periodic vector-bias malaria model incorporating the juvenile stage of mosquitoes and the use of ITNs. We derive the vector reproduction ratio $$R_v$$Rv and the basic reproduction ratio $$R_0$$R0. We show that the global dynamics of the model is completely determined by these two reproduction ratios. More precisely, the mosquito-free periodic solution is globally attractive if $$R_v<1$$Rv<1; the unique disease-free periodic solution is globally attractive if $$R_v>1$$Rv>1 and $$R_0<1$$R0<1; and the model admits a unique positive periodic solution and it is globally attractive if $$R_v>1$$Rv>1 and $$R_0>1$$R0>1. Numerically, we study the malaria transmission case in Port Harcourt, Nigeria. Our findings show that the use of ITNs has a positive effect on reducing $$R_0$$R0, and that malaria may be eliminated from this area if over 75% of the human population were to use ITNs. The simulation about the long term behavior of solutions has good agreement with the obtained analytic result. Moreover, we find that the ignorance of the vector-bias effect may result in underestimation of the basic reproduction ratio $$R_0$$R0. Another notable result is that the infection risk would be underestimated if the basic reproduction ratio $$[R_0]$$[R0] of the time-averaged autonomous system were used.