Transmission dynamics of multi-strain dengue virus with cross-immunity

Abstract

Since infection with one of the five strains of dengue virus produces life-long immunity to only this strain and temporary cross-immunity to other strains, we incorporated cross-immunity and exposed states for humans and mosquitoes in our compartmental model. We proved the globally and locally asymptotic stability of the disease-free equilibrium, the locally asymptotic stability of two boundary equilibria with the existence of only one strain, and the existence and uniqueness of the interior equilibrium with the coexistence of two strains. In addition, we found that the backward bifurcation exists. We evaluated the impact of parameters on the basic reproduction number by sensitivity analysis, and optimized the mitigation strategies according to Pontryagin’s Maximum Principle, taking into account corresponding costs. The numerical simulation results showed that increasing the economic costs may not always increase the effectiveness of optimal control, since the time for putting full control effort is shortened.