| Abstract: |
| In this paper, a deterministic model is proposed to perform a thorough investigation of
the transmission dynamics of Zika fever. Our model, in particular, takes into account the
e ects of horizontal as well as vertical disease transmission of both humans and vectors.
The expression for the basic reproductive number R0 is determined in terms of horizontal
as well as vertical disease transmission rates. An in-depth stability analysis of the model is
performed, and it is consequently shown, that model has a globally asymptotically stable
disease-free equilibrium when the basic reproduction number R0 < 1. It is also shown that
the disease strongly uniformly persists when R0 > 1 and in this case there exists a unique
endemic equilibrium which is locally asymptotically stable when R0 > 1.
Assuming infection prevalence in the population under the constant control, optimal
control theory is used to devise an optimal 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. |
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