Show simple item record

dc.contributor.advisorRíos-Soto, Karen R.
dc.contributor.authorMelo-Pantoja, Daniel A.
dc.date.accessioned2019-01-17T18:38:55Z
dc.date.available2019-01-17T18:38:55Z
dc.date.issued2018
dc.identifier.urihttps://hdl.handle.net/20.500.11801/1705
dc.description.abstractEl Zika es una enfermedad infecciosa desarrollada por el Virus del Zika (ZIKV por sus siglas en ingles), la cual ha estado, alertando a las regiones tropicales y subtropicales en los ultimos a~nos. La enfermedad es conocida como una infeccion que puede ser trasmitida por va sexual o mediante un vector, en este caso un mosquito [4]. Es muy conocido que los sntomas son se~nales que permiten deducir el desarrollo de algun tipo de enfermedad. Sin embargo, no siempre el cuerpo humano produce sntomas cuando es atacado por un virus o bacteria. Este es el caso de enfermedades asintomaticas, pues son difciles de diagnosticar y en consecuencia de tratar. Desafortunadamente, en muchos casos, las infecciones asintomaticas son detectadas cuando la enfermedad ya ha causado mucho da~no de forma silenciosa. El Zika es una enfermedad sintomatica en el 20% de los casos y asintomatica en el restante 80%. Debido a esto y con la motivacon de trabajos anteriores, en esta investigacion se estudia la dinamica de la transmision vectorial y sexual del ZIKV considerando individuos infectados sintomaticos y asintomaticos. El modelo propuesto incluye un parametro de alteracion de infecciosidad, el cual permitira estudiar todos los posibles casos de infecciosidad desconocida al presente, analizar su efecto en la poblacion y entender el rol de los asintomaticos, no solo bajo transmision vectorial, si no tambien por transmision sexual. Para esto, se formulo y estudio un modelo matematico epidemiologico compuesto de ocho estados. Los ocho estados representan las diferentes etapas que un humano y un mosquito con el ZIKV puede experimentar. Se obtiene el numero reproductivo basico R0, se realiza el analisis cualitativo y numerico del sistema para valores de parametros tomados de la literatura, as como tambien, se realiza el analisis de sensibilidad de parametros al R0. Existen dos puntos de equilibrio en el sistema, el libre de Zika y el endemico. El analisis numerico predice una epidemia, donde el numero de infectados (incidencia) puede crecer o decrecer dependiendo de los valores asignados a cada parametro. Por lo tanto, esfuerzos para controlar una epidemia podran enfocarse en reducir la tasa de infeccion de mosquito a humano, la tasa de transmision sexual y controlar de manera oportuna la cantidad de individuos asintomaticos en la poblacion. Cuando el numero reproductivo basico de transmision vectorial es mas grande que el de transmision sexual hay un retardo en el que el virus invada la poblacion y bajo este escenario existen oportunidades para prevenir una epidemia del ZIKV con medidas preventivas como insecticidas, repelentes, condones, etc. R0 es mas sensitivo a la tasa de mortalidad del mosquito y a la tasa de transmision vectorial, por lo tanto la mejor manera de prevenir y controlar un brote del ZIKV es disminuyendo el numero de mosquitos en la poblacion e iniciando campa~nas para que cada individuo elimine los criaderos. Esta investigacion tambien sugiere campa~nas para detectar los infectados (ya sea asintomaticos o sintomaticos) por el ZIKV y aislarlos, a tiempo.en_US
dc.description.abstractZika is an infectious disease developed by the Zika Virus (ZIKV), which has been alarming people during the last few years in tropical and subtropical regions. It is known as an infection that can be transmitted both sexually and through a vector, in this case a mosquito [4]. It is well known that symptoms are signals that allow to deduce the development of some type of disease. However, the human body does not always produce symptoms when attacked by a virus or bacterium. This is the case of asymptomatic diseases, a fact that makes them diffcult to diagnose and, in consequence, to treat. Unfortunately, in many cases, the asymptomatic infected are detected when the disease has done much damage silently. Zika is symptomatic in the 20% of cases and asymptomatic in the remaining 80%. Because of this and through the motivation of previous works, this research analyzes the dynamics of the vector and sexual transmissions of ZIKV in symptomatic and asymptomatic infected individuals. The model proposed includes a parameter of alteration of infectiousness that will allow to study all possible cases of presently unknown infections, to analyze its effect on the population, and to understand the role of asymptomatic humans, not only under vector transmission but also considering sexual transmission. Thus, a mathematical epidemiological model composed of eight stages was formulated and studied. The eight stages represent the different phases that humans and mosquitoes with ZIKV may experience. The basic reproductive number R0 was obtained and the qualitative and numerical analysis of the system were done for values of parameters taken from the literature, as well as the sensitivity analysis of parameters, thus obtaining two equilibrium points, the Zika-free equilibrium and the endemic equilibrium. The numerical analysis predicts an epidemic, where the number of infected can grow or decrease depending on the value of key parameters. Therefore, efforts to control an epidemic could focus on reducing the mosquito-to-human infection, sexual transmission rate, and the control, in a timely manner, of the number of asymptomatic individuals in the population. When the vector transmission ratio is larger than the sexual transmission ratio, there is a time delay for ZIKV to invade the population. Under this scenario there is a window of opportunities to prevent an epidemic of ZIKV with preventive measures, such as insecticide, repellents, condoms, among others. R0 is more sensitive to the mosquito mortality rate and vector transmission rate; therefore, the best way to prevent and control an outbreak of the ZIKV is by decreasing the number of mosquitoes in the population and initiating campaigns for each individual to eliminate the breeding sites. This research also suggests campaigns to detect those infected-whether asymptomatic or symptomatic-with the ZIKV and isolate them on Time.en_US
dc.language.isoEnglishen_US
dc.subjectZikaen_US
dc.subject<odelen_US
dc.subjectSexual transmissionen_US
dc.titleA mathematical model for ZIKA virus and the effects of variable infectivity on the asymptomatic and symptomatic infected humanen_US
dc.typeThesisen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c) 2018 Daniel A. Melo-Pantojaen_US
dc.contributor.committeeSteinberg, Lev
dc.contributor.committeeSantana Morant, Damaris
dc.contributor.representativeCruzado, Ivette
thesis.degree.levelM.S.en_US
thesis.degree.disciplineApplied Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences – Sciencesen_US
dc.contributor.departmentDepartment of Mathematicsen_US
dc.description.graduationSemesterSpring (2nd semester)en_US
dc.description.graduationYear2018en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

  • Theses & Dissertations
    Items included under this collection are theses, dissertations, and project reports submitted as a requirement for completing a degree at UPR-Mayagüez.

Show simple item record

All rights reserved
Except where otherwise noted, this item's license is described as All Rights Reserved