A study on Zika–Dengue coinfection model with microcephaly newborn dynamics

Abstract

A study of data on the Zika outbreak in Brazil in 2015–2016 provides knowledge that Zika infection can trigger brain disorders such as Guillain–Barré Syndrome in adults and microcephaly in newborns. Zika infection is a vector-borne disease most commonly transmitted to humans through an infected Aedes mosquito bite, which is also the primary vector for dengue. Thus, many cases of these two diseases were recorded in the same population. In this study, we formulated a Zika–dengue coinfection model that describes the combined dynamics of Zika and dengue, involving the birth of microcephaly-malformed infants from pregnant women infected with the Zika virus. The analysis of the model states that three equilibrium points can be calculated explicitly, namely a disease-free equilibrium point and two boundary endemic equilibrium points. In addition, there is one implicit coinfection equilibrium point. The basic reproduction number is obtained along with the stability of disease-free equilibrium. Condition for the instability of the two boundary equilibria is obtained. This condition allows for a bifurcation point in the numerical exploration of the coinfection equilibrium point and its stability properties. The numerical simulation shows that the coinfection point appears when the two boundary equilibria are unstable. In addition, two Hopf bifurcation points are found with stable limit cycles between them.