Dengue fever spreading based on probabilistic cellular automata with two lattices

Modeling and simulation of mosquito-borne diseases have gained attention due to a growing incidence in tropical countries in the past few years. Here, we study the dengue spreading in a population modeled by cellular automata, where there are two lattices to model the human-mosquitointeraction: one lattice for human individuals, and one lattice for mosquitoes in order to enable different dynamics in populations. The disease considered is the dengue fever with one, two or three different serotypes coexisting in population. Although many regions exhibit the incidence of only one serotype, here we set a complete framework to also study the occurrence of two and three serotypes at the same time in a population. Furthermore, the flexibility of the model allows its use to other mosquito-borne diseases, like chikungunya, yellow fever and malaria. An approximation of the cellular automata is proposed in terms of ordinary differential equations; the spreading of mosquitoes is studied and the influence of some model parameters are analyzed with numerical simulations. Finally, a method to combat dengue spreading is simulated based on a reduction of mosquito birth and mosquito bites in population.