Luna Alvear, Alibeth E.

Profile Picture

Filters

20211
Reset filters

Settings

Citations

Publication Search Results

Now showing 1 - 1 of 1
  • Thumbnail Image
    Publication
    A mathematical model on the spatial spread of Zika virus
    (2021-05-14) Luna Alvear, Alibeth E.; Ríos Soto, Karen R.; College of Arts and Sciences - Sciences; Rozga, Krzysztof; Steinberg, Lev; Department of Mathematics; Boglio Martínez, Rafael
    Zika virus, which belongs to the Flavivirus genus, of the Flaviviridae family, is transmitted by the bite of the female Aedes Aegypti mosquitoes (vectors), as well as sexually, although in laver quantities. This disease was first identified in Macacos (Uganda, 1947) and spread in the Americas region in mid-2015. Since then, outbreaks have occurred in multiple countries and territories in South America and the Caribbean. According to the World Health Organization (WHO) and Puerto Rico Department of Health (PRDH), the first locally acquired case of Zika virus disease in Puerto Rico was identified in early December 2015 and by 2016 a total of 35,395 cases were reported on the island. In this work, a mathematical model is proposed to study the spatial dissemination of the Zika virus using a system of partial differential equations of the reaction-diffusion-advection type. The populations considered are the human and mosquito population, for which we characterize subclasses of individuals based on their epidemiological status (susceptible, infected, and recovered for the human population and susceptible and infected for the mosquito population). To describe the localized spread of the Zika virus during a short period of epidemic, the human population is considered homogeneously distributed in space. The system equilibria are then calculated, as well as the threshold condition R0 based on the model parameters; this condition helps determine the possible spread of Zika virus and the risk of outbreaks. The analysis is followed by studying the reaction-diffusion-advection model assuming traveling wave solutions that, in turn, allow to calculate a minimum speed of virus propagation. On the other hand, with parameters for the model obtained from the literature, numerical simulations are performed to study the behavior of the traveling waves.