Three-dimensional spread analysis of a Dengue disease model with numerical season control

Dengue is among the most important infectious diseases in the world. The main contribution of our paper is to present a mixed system of partial and ordinary differential equations. This combined model is a generalization of the two presented mathematical models (A. L. de Araujo, J. L. Boldrini and B. M. Calsavara, An analysis of a mathematical model describing the geographic spread of dengue disease, J. Math. Anal. Appl. 444 (2016) 298-325) and (L. Cai, X. Li, N. Tuncer, M. Martcheva and A. A. Lashari, Optimal control of a malaria model with asymptomatic class and superinfection, Math. Biosci. 288 (2017) 94-108), describing the geographic spread of dengue disease. Our model has the ability to consider the possibility of asymptomatic infection, which leads to investigate the effect of dengue asymptomatic individuals on disease dynamics and to go into the possibility of superinfection of asymptomatic individuals. In the light of considering these factors, as well as the movements of human and mature female mosquitoes, more realistic modeling of dengue disease can be achieved. We present a mathematical analysis and show the global existence of a unique non-negative solution to this model and then establish ways to control dengue disease using numerical simulations and sensitivity analysis of model parameters (which are related to the contact rates and death rate of winged mosquitoes). To show different biological behaviors, we provide several numerical results, showing the role of parameters in controlling dengue disease transmission. From our numerical simulations, it can also be concluded that local control of dengue transmission can be done at a lower cost.