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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 diseasefree 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 viceversa. 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 nonagestructured model then introduced agestructure 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 nonagestructured and agestructured analyses introducing seasonality into the A. aegypti birth function to model the effect of these environmental factors.
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 nonagestructured model then introduced agestructure 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 nonagestructured and agestructured analyses introducing seasonality into the A. aegypti birth function to model the effect of these environmental factors.
Original language  English 

Pages (fromto)  8217–8242 
Number of pages  26 
Journal  Mathematical Biosciences and Engineering 
Volume  16 
Issue number  6 
DOIs  
Publication status  Published  16 Sept 2019 
Keywords
 Zika virus
 microcephaly
 dengue
 aedes aegypti
 parameter estimation
 least square estimation
 ordinary differential equations
 partial differential equations
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 1 Finished

EPSRC Institutional Sponsorship: Global Challenges Research Fund (GCRF) / R160677105
EPSRC (Engineering and Physical Sciences Research Council)
1/06/16 → 31/03/17
Project: Research  Internally Allocated