Estimation of the expected number of cases of microcephaly in Brazil as a result of Zika

Yanfeng Liang; David Greenhalgh; Yanfeng Liang; David Greenhalgh

doi:10.3934/mbe.2019416

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 8217-8242. doi: 10.3934/mbe.2019416

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Research article

Estimation of the expected number of cases of microcephaly in Brazil as a result of Zika

Yanfeng Liang ^,,
David Greenhalgh

Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, UK

Received: 07 June 2019 Accepted: 22 August 2019 Published: 16 September 2019

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.
- Zika virus,
- microcephaly,
- dengue,
- Aedes aegypti,
- parameter estimation,
- least square estimation,
- ordinary differential equations,
- partial differential equations
Citation: Yanfeng Liang, David Greenhalgh. Estimation of the expected number of cases of microcephaly in Brazil as a result of Zika[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 8217-8242. doi: 10.3934/mbe.2019416

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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 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.

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