Analyzing the dynamics and optimal control of a vector-borne model with dual vertical transmission and multiple serotypes

Transmission and contact patterns have an important influence on the intensity and trend of disease transmission. Taking into account two different serotypes and the vertical transmission of the disease in both humans and mosquitoes, this paper proposes a novel vector-borne disease model. In order to explore the evolution mechanisms of the model and the impacts of contact pattern on disease transmission. The basic regeneration number of the proposed model is obtained via the next-generation matrix approach. Subsequently, we analyze the conditions of the stabilities and existences of the equilibrium points. Further, the sensitivity of the parameters is studied using numerical simulations. It is observe that the increase of vertical transmission rate of mosquitoes leads to the increase of the basic reproduction number. In addition, we develop vaccination and insecticide control strategies and derive the existence and expression of the optimal solution. Our numerical results show that vaccination has a little effect on preventing the spread of disease among mosquitoes. However, insecticide spraying is effective in reducing the spread of disease between humans and mosquitoes.