On the co-infection of dengue fever and Zika virus

Abstract

In this paper, we present a co-infection mathematical model for dengue-Zika disease in order to carry out their synergistic relationship in the presence of prevention and treatment. Submodel analysis is investigated to establish the reproduction numbers for each disease and to determine the disease-free local stability equilibrium status. The endemic disease equilibrium is investigated using bifurcation analysis and shows backward bifurcation. We use Pontryagin's maximum principle to explore and determine the best optimal strategies to control both diseases. Numerical optimal control analysis indicates that effective prevention and treatment of each disease will help in the effective control and eradication of the diseases. Finally, the control of co-infection of dengue-Zika requires that communities should combine both prevention and treatment associated with each disease at the same time.