Abstract
In this paper we have adapted a delayed dengue model to Zika. By assuming that the epidemic starts by a single infected individual entering a disease-free population at some initial time t0 we have used the least squares parameter estimation technique in R to estimate the initial time t0 using observed Zika data from Brazil as well as the transmission probabilities of Zika in Brazil between humans and mosquitoes and vice-versa. Different values of Aedes aegypti (A. aegypti) biting rate are used throughout the paper. We have estimated the value of the basic reproduction number for Zika in Brazil and calculated the expected number of cases of microcephaly in newborns as a result of women infected with Zika during pregnancy. We started off with a non-age-structured model then introduced age-structure into the model. However in reality seasonality, in particular temperature and rainfall, have a great impact on the population size of A. aegypti. Hence we repeat both the non-age-structured and age-structured analyses introducing seasonality into the A. aegypti birth function to model the effect of these environmental factors.
Highlights
The Zika virus is spread by the same species of mosquito, namely Aedes aegypti (A. aegypti), as dengue
We have estimated the value of the basic reproduction number for Zika in Brazil and calculated the expected number of cases of microcephaly in newborns as a result of women infected with Zika during pregnancy
We focus on analysing the effect of pregnant women infected with Zika virus during their first trimester as various reports (e.g. [22, 23]) suggest that pregnant women who are infected with the Zika virus during the first trimester have a much higher risk of their babies developing microcephaly as opposed to those who are infected with Zika in their second or third trimesters
Summary
The Zika virus is spread by the same species of mosquito, namely Aedes aegypti (A. aegypti), as dengue. In this paper we will use an existing mathematical model for dengue to analyse the dynamical behaviour for the Zika virus, especially in Brazil, as well as obtaining the future expected number of cases of microcephaly due to Zika. We will use four different approaches to estimate the expected number of cases of microcephaly in Brazil due to pregnant women exposed to the Zika virus. This paper is arranged as follows: In Section 2, we will look at the first approach by working with a delayed dengue model without seasonality as well as defining the parameter values. Numerical simulations are produced throughout the paper to illustrate our findings
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