A deterministic model for the transmission dynamics of Zika is designed and rigorously analysed. A model consisting of mutually exclusive compartments representing the human and mosquito dynamics takes into account both direct (human‐human) and indirect modes of transmissions. The basic offspring number of the mosquito population is computed and condition for existence and stability of equilibria is investigated. Using the centre manifold theory, the model (with and without direct transmission) is shown to exhibit the phenomenon of backward bifurcation (where a locally asymptotically stable disease free equilibrium coexists with a locally asymptotically stable endemic equilibrium) whenever the associated reproduction number is less than unity. The study shows that the models with and without direct transmission exhibit the same qualitative dynamics with respect to the local stability of their associated disease‐free equilibrium and backward bifurcation phenomenon. The main cause of the backward bifurcation is identified as Zika induced mortality in humans. Sensitivity (local and global) analysis of the model parameters are conducted to identify crucial parameters that influence the dynamics of the disease. Analysis of the model shows that an increase in the mating rate with sterile mosquito decreases the mosquito population. Numerical simulations, using parameter values relevant to the transmission dynamics of Zika are carried out to support some of the main theoretical findings.South African DST/NRF SARChI chair on Mathematical Models and Methods in Bioengineering and Biosciences (M3B2) and DST-NRF Centre of Excellence in Mathematical and Statisti-cal Sciences (CoE-MaSS).http://wileyonlinelibrary.com/journal/mma2019-12-01hj2019Mathematics and Applied Mathematic
