ABSTRACT
This chapter deals with seven models of transmission and outbreak dynamics of Zika virus. The first four models discuss the temporal dynamics and the remaining three models discuss the temporal and spatial dynamics. Model 1 is an SIR model for transmission of the Zika virus to humans, which discusses some optimal control strategies for prevention, treatment, and use of an insecticide. Model 2 is an SEIR transmission model (modification of the SIR model), which considers human-to-human as well as the vector (mosquito)-to-human transmissions. Model 3 is a deterministic SEIR model that investigates the transmission dynamics of Zika virus including the horizontal and vertical modes of transmission in both human and vector populations. The occurrence of the backward bifurcation phenomenon for a large vector population is shown. Model 4 studies the transmission dynamics of the virus using a compartmental framework that includes vector-borne and human vertical transmission (both heterosexual and homosexual) of Zika virus, the birth of babies with microcephaly, and asymptotically infected individuals. Model 5 is an SIR transmission model that considers the influence of human and vector mobility and human–mosquito interaction in space and time. In Model 6, the Zika virus transmission model with criss-cross interactions is discussed to understand how spatial heterogeneities of the vector and host populations influenced the dynamics of the outbreak of Zika virus in Rio de Janeiro, Brazil. In Model 7, the spatiotemporal dynamics of an SEIR transmission model is discussed and the possible scenario of the spread of the virus is presented.
