Modeling effects of impulsive control strategies on the spread of mosquito borne disease: role of latent period

Controlling the mosquito population is a big challenge for humans. In this paper, we have studied the effects of impulsive control strategies on the spread of mosquito-borne diseases considering the latent period. Therefore, we proposed and analyzed a mosquito-borne disease model governed by a system of impulsive delay differential equations. The proposed mosquito-borne disease model also accounts for three different impulsive control strategies, namely vaccination, pesticides, and adulticides. Two thresholds $$R_1$$ and $$R_2$$ established for the global attractivity of the disease-free state and the persistence of the endemic state. The non-trivial disease-free solution of the proposed model is globally asymptotically stable if $$R_1$$ and $$R_2$$ less than one. It is shown that a unique positive endemic periodic solution exists only when $$ R_1 $$ and $$ R_2$$ greater than unity, which makes for the persistence of the disease. Numerical simulation supports the analytical finding and shows the effectiveness of the impulse control strategies.