SIR Model of Spread of Zika Virus Infections: ZIKV Linked to Microcephaly Simulations

Abstract

An SIR model of Zika virus (ZIKV) spread is formulated that includes ZIKV infections to newborns. Analytically, the model has one disease free and one endemic equilibrium point. The free one is stable for some conditions when and unstable when . In Brazil, when ZIKV infections expand and for diminishes. There were 67 microcephaly babies confirmed to have linked with ZIKV infections as of February 2016 in Brazil. Simulation predicts that the number rose to not less than 2100 in January 2017 and expected to increase around 4350 by January 2018 if not controlled. Simulation of the endemic equilibrium point indicates that there is more number of individuals in the recovered class than in the infectious class contrasting the initial state of the epidemic. This recovered class serves as a silent natural resistance against spread of the epidemic. Measures to control ZIKV infections have been suggested by analyzing parameters linked to transmission. The base is controlling basic reproduction number ( ) of the model. There are parameters for human-mosquito transmission and some for sexual-transmission factor. It appears that controlling spread of ZIKV infections by human-mosquito transmission may greatly reduce the value of .