Abstract

An SIR model of Zika virus (ZIKV) spread is formulated that includes ZIKV infections to newborns. Analytically, the model has one disease free and one endemic equilibrium point. The free one is stable for some conditions when R0 and unstable when R0>1. In Brazil, when R0≈2>1 ZIKV infections expand and for R0 = 0.875R0) of the model. There are parameters for human-mosquito transmission and some for sexual-transmission factor. It appears that controlling spread of ZIKV infections by human-mosquito transmission may greatly reduce the value of R0.

Highlights

  • As of June 2016, around 500,000 Zika virus disease (ZVD) cases have been estimated in Brazil, and autochthonous circulation has been observed in 40 countries from the Americas [8]

  • Up to February 27, 2016; 67 newborns with microcephaly were confirmed to have been due to Zika virus (ZIKV) infections

  • There are at least 2100 in total of babies who have been ZIKV infected by January 2017, this number is expected to rise up about 4350 by January 2018 (Figure 7(a))

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Summary

Historical Background

On February 1st, 2016, the World Health Organization declared ZIKV epidemic in the Americas as a Public Health Emergency of International Concern. Little clinical importance was attributed to ZIKV, for the reason that only few symptomatic cases were reported in some African and Southeast Asiatic countries at the time [14] This situation changed in 2007, when a large outbreak was registered on the Yap Island, Micronesia, caused by the Asian ZIKV lineage. At the arrival of summer season in the northern hemisphere is the most suitable time when Aedes mosquitoes in Europe find optimum climate to get infected by ZIKV and later transmit this virus to tourists and into local population through biting [17] At this point, it is relevant to cover and analyze the monthly traffic of travelers by air, arriving into the cities of Europe from the Zika affected regions of both the American continents and Europe. As of June 2016, around 500,000 Zika virus disease (ZVD) cases have been estimated in Brazil, and autochthonous circulation has been observed in 40 countries from the Americas [8]

Mathematical Background
Model Formulation
Existence of the Endemic Equilibrium
Model Simulations
Fitting the Model into Brazil ZIKV Infections State
Natural Resistance Against ZIKV Epidemics
Intervention for Epidemic Elimination
Findings
Conclusions
Full Text
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