Problems in the theory and application of models of infectious diseases

• Main Author: Hernandez-Suarez, Carlos Moises
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-1997
• Subjects: Biostatistics; Ecology; Public health
• ISBN: 9780591549836; 0591549832

Chapter 1 establishes a mathematical result that can be used to find the numerical solution of the time to extinction of birth-death continuous time Markov chains, as well as the expected value of the integral under the stochastic path. Examples of applications to classical birth-death processes and to the Susceptible- Infected- Susceptible stochastic epidemic models are discussed. Some stochastic processes have a set of absorbing states and will eventually reach a member of this set. Since the time to absorption could be infinite, it is useful to study the evolution of the process not having reached an absorbing state, that is, we focus on the study of the quasistationary distribution. Chapter 2 shows that under certain mild conditions, good approximations to the quasistationary distribution for Susceptible- Infected- Susceptible (SIS) and Susceptible- Latent- Infected- Susceptible (SEIS) epidemic models can be analyzed using results from queuing theory. Measuring vaccine efficacy is an area that has gained much attention in the last ten years. In real life situations, individuals do not mix homogeneously among themselves, which imposes the problem of accounting for the possibility that individuals have not been subjected to the same amount of exposure to infection, resulting in bias when measuring vaccine efficacy. Chapter 3 shows that for a stochastic epidemic model, the usual method for estimating vaccine efficacy in a stratified population with homogeneous mixing can be adapted to estimate vaccine efficacy under non-homogeneous mixing. Chapter 4 deals with a specific application, the control of Chagas disease in small villages, which is usually managed through periodic campaigns or by providing individuals with the tools and chemicals to perform it by themselves periodically. In Chapter 4 an analysis of self-applied control measures that focuses on the frequency of control required to eradicate the vector of the community is done.