Matching Items (2)
Description
Mathematical modeling of infectious diseases can help public health officials to make decisions related to the mitigation of epidemic outbreaks. However, over or under estimations of the morbidity of any infectious disease can be problematic. Therefore, public health officials can always make use of better models to study the potential implication of their decisions and strategies prior to their implementation. Previous work focuses on the mechanisms underlying the different epidemic waves observed in Mexico during the novel swine origin influenza H1N1 pandemic of 2009 and showed extensions of classical models in epidemiology by adding temporal variations in different parameters that are likely to change during the time course of an epidemic, such as, the influence of media, social distancing, school closures, and how vaccination policies may affect different aspects of the dynamics of an epidemic. This current work further examines the influence of different factors considering the randomness of events by adding stochastic processes to meta-population models. I present three different approaches to compare different stochastic methods by considering discrete and continuous time. For the continuous time stochastic modeling approach I consider the continuous-time Markov chain process using forward Kolmogorov equations, for the discrete time stochastic modeling I consider stochastic differential equations using Wiener's increment and Poisson point increments, and also I consider the discrete-time Markov chain process. These first two stochastic modeling approaches will be presented in a one city and two city epidemic models using, as a base, our deterministic model. The last one will be discussed briefly on a one city SIS and SIR-type model.
ContributorsCruz-Aponte, Maytee (Author) / Wirkus, Stephen A. (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Camacho, Erika T. (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
This work is an assemblage of three applied projects that address the institutional and spatial constraints to managing threatened and endangered (T & E) terrestrial species. The first project looks at the role of the Endangered Species Act (ESA) in protecting wildlife and whether banning non–conservation activities on multi-use federal lands is socially optimal. A bioeconomic model is used to identify scenarios where ESA–imposed regulations emerge as optimal strategies and to facilitate discussion on feasible long–term strategies in light of the ongoing public land–use debate. Results suggest that banning harmful activities is a preferred strategy when valued species are in decline or exposed to poor habitat quality. However such a strategy cannot be sustained in perpetuity, a switch to land–use practices characteristic of habitat conservation plans is recommended. The spatial portion of this study is motivated by the need for a more systematic quantification and assessment of landscape structure ahead of species reintroduction; this portion is further broken up into two parts. The first explores how connectivity between habitat patches promotes coexistence among multiple interacting species. An agent–based model of a two–patch metapopulation is developed with local predator–prey dynamics and density–dependent dispersal. The simulation experiment suggests that connectivity levels at both extremes, representing very little risk and high risk of species mortality, do not augment the likelihood of coexistence while intermediate levels do. Furthermore, the probability of coexistence increases and spans a wide range of connectivity levels when individual dispersal is less probabilistic and more dependent on population feedback. Second, a novel approach to quantifying network structure is developed using the statistical method of moments. This measurement framework is then used to index habitat networks and assess their capacity to drive three main ecological processes: dispersal, survival, and coexistence. Results indicate that the moments approach outperforms single summary metrics and accounts for a majority of the variation in process outcomes. The hierarchical measurement scheme is helpful for indicating when additional structural information is needed to determine ecological function. However, the qualitative trend between network indicator and function is, at times, unintuitive and unstable in certain areas of the metric space.
ContributorsSalau, Kehinde Rilwan, 1985- (Author) / Janssen, Marco A (Thesis advisor) / Fenichel, Eli P (Thesis advisor) / Anderies, John M (Committee member) / Abbott, Joshua K (Committee member) / Arizona State University (Publisher)
Created2013