Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil

Zika virus infection on humans is mainly caused by the bite of an infected Aedes mosquito, either A. aegypti or A. albopictus. The infection on human usually causes rash, mild fever, conjunctivitis, and muscle pain. These symptoms are quite similar to dengue and chikungunya diseases, which can be transmitted by the same mosquitoes. Other modes of transmission of Zika disease have been observed, as sexual transmission, though less common [1]. Such modes of transmission are included in mathematical models found in the recent literature: see [2, Section 8] for a good state of the art. The name of the virus comes from the Zika forest in Uganda, where the virus was isolated for the first time in 1947. Up to very recent times, most of the Zika outbreaks have occurred in Africa with some sporadic outbreaks in Southeast Asia and also in the Pacific Islands. Since May 2015, Zika virus infections have been confirmed in Brazil and, since October 2015, other countries and territories of the Americas have reported the presence of the virus: see [3], where evolutionary trees, constructed using both newly sequenced and previously available Zika virus genomes, reveal how the recent outbreak arose in Brazil and spread across the Americas. The subject attracted a lot of attention and is now under strong current investigations. In [4], a deterministic model, based on a system of ordinary differential equations, was proposed for the study of the transmission dynamics of the Zika virus. The model incorporates mother-to-child transmission as well as the development of microcephaly in newly born babies. The analysis shows that the disease-free equilibrium of the model is locally and globally asymptotically stable, whenever the associated reproduction number is less than one, and unstable otherwise. A sensitivity analysis was carried out showing that the mosquito biting, recruitment and death rates, are among the parameters with the strongest impact on the basic reproduction number. Then, some control strategies were proposed with the aim to reduce such values [4]. A two-patch model, where host-mobility is modeled using a Lagrangian approach, is used in [1], in order to understand the role of host-movement on the transmission dynamics of Zika virus in an idealized environment. Here we are concerned with the situation in Brazil and its consequences on brain anomalies, in particular microcephaly, which occur in fetuses of infected pregnant woman. This is a crucial question as far as the main problem related with Zika virus is precisely the number of neurological disorders and neonatal malformations [5]. Our study is based on the Zika virus situation reports for Brazil, as publicly available at the World Health Organization (WHO) web page. Based on a systematic review of the literature up to 30th May 2016, the WHO has concluded that Zika virus infection during pregnancy is a cause of congenital brain abnormalities, including microcephaly. Moreover, another important conclusion of the WHO is that the Zika virus is a trigger of Guillain-Barré syndrome [6]. Our analysis is focused on the number of confirmed cases of Zika in Brazil. For this specific case, an estimate of the population of the country is known, as well as the number of