Coexistence of different serotypes of dengue virus

We formulate a non-linear system of differential equations that models the dynamics of dengue fever. This disease is produced by any of the four serotypes of dengue arbovirus. Each serotype produces permanent immunity to it, but only a certain degree of cross-immunity to heterologous serotypes. In our model we consider the relation between two serotypes. Our interest is to analyze the factors that allow the invasion and persistence of different serotypes in the human population. Analysis of the model reveals the existence of four equilibrium points, which belong to the region of biological interest. One of the equilibrium points corresponds to the disease-free state, the other three equilibria correspond to the two states where just one serotype is present, and the state where both serotypes coexist, respectively. We discuss conditions for the asymptotic stability of equilibria, supported by analytical and numerical methods. We find that coexistence of both serotypes is possible for a large range of parameters.