Mathematical analysis of the role of hospitalization/isolation in controlling the spread of Zika fever

An in-depth stability analysis of the model is performed, and it is consequently shown, that the model has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R0 < 1. It is also shown that when R0 > 1, there exists a unique endemic equilibrium. We showed that the endemic equilibrium point is globally asymptotically stable when it exists. We were able to prove this result in a reduced model. Furthermore, we conducted an uncertainty and sensitivity analysis to recognize the impact of crucial model parameters on R0. The uncertainty analysis yields an estimated value of the basic reproductive number R0 = 1.54. Assuming infection prevalence in the population under constant control, optimal control theory is used to devise an optimal hospitalization/isolation control strategy for the model. The impact of isolation on the number of infected individuals and the accumulated cost is assessed and compared with the constant control case.