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Description
In the field of infectious disease epidemiology, the assessment of model robustness outcomes plays a significant role in the identification, reformulation, and evaluation of preparedness strategies aimed at limiting the impact of catastrophic events (pandemics or the deliberate release of biological agents) or used in the management of disease prevention strategies, or employed in the identification and evaluation of control or mitigation measures. The research work in this dissertation focuses on: The comparison and assessment of the role of exponentially distributed waiting times versus the use of generalized non-exponential parametric distributed waiting times of infectious periods on the quantitative and qualitative outcomes generated by Susceptible-Infectious-Removed (SIR) models. Specifically, Gamma distributed infectious periods are considered in the three research projects developed following the applications found in (Bailey 1964, Anderson 1980, Wearing 2005, Feng 2007, Feng 2007, Yan 2008, lloyd 2009, Vergu 2010). i) The first project focuses on the influence of input model parameters, such as the transmission rate, mean and variance of Gamma distributed infectious periods, on disease prevalence, the peak epidemic size and its timing, final epidemic size, epidemic duration and basic reproduction number. Global uncertainty and sensitivity analyses are carried out using a deterministic Susceptible-Infectious-Recovered (SIR) model. The quantitative effect and qualitative relation between input model parameters and outcome variables are established using Latin Hypercube Sampling (LHS) and Partial rank correlation coefficient (PRCC) and Spearman rank correlation coefficient (RCC) sensitivity indices. We learnt that: For relatively low (R0 close to one) to high (mean of R0 equals 15) transmissibility, the variance of the Gamma distribution for the infectious period, input parameter of the deterministic age-of-infection SIR model, is key (statistically significant) on the predictability of the epidemiological variables such as the epidemic duration and the peak size and timing of the prevalence of infectious individuals and therefore, for the predictability these variables, it is preferable to utilize a nonlinear system of Volterra integral equations, rather than a nonlinear system of ordinary differential equations. The predictability of epidemiological variables such as the final epidemic size and the basic reproduction number are unaffected by (or independent of) the variance of the Gamma distribution for the infectious period and therefore for the choice on which type of nonlinear system for the description of the SIR model (VIE's or ODE's) is irrelevant. Although, for practical proposes, with the aim of lowering the complexity and number operations in the numerical methods, a nonlinear system of ordinary differential equations is preferred. The main contribution lies in the development of a model based decision-tool that helps determine when SIR models given in terms of Volterra integral equations are equivalent or better suited than SIR models that only consider exponentially distributed infectious periods. ii) The second project addresses the question of whether or not there is sufficient evidence to conclude that two empirical distributions for a single epidemiological outcome, one generated using a stochastic SIR model under exponentially distributed infectious periods and the other under the non-exponentially distributed infectious period, are statistically dissimilar. The stochastic formulations are modeled via a continuous time Markov chain model. The statistical hypothesis test is conducted using the non-parametric Kolmogorov-Smirnov test. We found evidence that shows that for low to moderate transmissibility, all empirical distribution pairs (generated from exponential and non-exponential distributions) for each of the epidemiological quantities considered are statistically dissimilar. The research in this project helps determine whether the weakening exponential distribution assumption must be considered in the estimation of probability of events defined from the empirical distribution of specific random variables. iii) The third project involves the assessment of the effect of exponentially distributed infectious periods on estimates of input parameter and the associated outcome variable predictions. Quantities unaffected by the use of exponentially distributed infectious period within low transmissibility scenarios include, the prevalence peak time, final epidemic size, epidemic duration and basic reproduction number and for high transmissibility scenarios only the prevalence peak time and final epidemic size. An application designed to determine from incidence data whether there is sufficient statistical evidence to conclude that the infectious period distribution should not be modeled by an exponential distribution is developed. A method for estimating explicitly specified non-exponential parametric probability density functions for the infectious period from epidemiological data is developed. The methodologies presented in this dissertation may be applicable to models where waiting times are used to model transitions between stages, a process that is common in the study of life-history dynamics of many ecological systems.
ContributorsMorales Butler, Emmanuel J (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Aparicio, Juan P (Thesis advisor) / Camacho, Erika T (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
Extraordinary medical advances have led to significant reductions in the burden of infectious diseases in humans. However, infectious diseases still account for more than 13 million annual deaths. This large burden is partly due to some pathogens having found suitable conditions to emerge and spread in denser and more connected host populations, and others having evolved to escape the pressures imposed by the rampant use of antimicrobials. It is then critical to improve our understanding of how diseases spread in these modern landscapes, characterized by new host population structures and socio-economic environments, as well as containment measures such as the deployment of drugs. Thus, the motivation of this dissertation is two-fold. First, we study, using both data-driven and modeling approaches, the the spread of infectious diseases in urban areas. As a case study, we use confirmed-cases data on sexually transmitted diseases (STDs) in the United States to assess the conduciveness of population size of urban areas and their socio-economic characteristics as predictors of STD incidence. We find that the scaling of STD incidence in cities is superlinear, and that the percent of African-Americans residing in cities largely determines these statistical patterns. Since disparities in access to health care are often exacerbated in urban areas, within this project we also develop two modeling frameworks to study the effect of health care disparities on epidemic outcomes. Discrepant results between the two approaches indicate that knowledge of the shape of the recovery period distribution, not just its mean and variance, is key for assessing the epidemiological impact of inequalities. The second project proposes to study, from a modeling perspective, the spread of drug resistance in human populations featuring vital dynamics, stochasticity and contact structure. We derive effective treatment regimes that minimize both the overall disease burden and the spread of resistance. Additionally, targeted treatment in structured host populations may lead to higher levels of drug resistance, and if drug-resistant strains are compensated, they can spread widely even when the wild-type strain is below its epidemic threshold.
ContributorsPatterson-Lomba, Oscar (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Towers, Sherry (Thesis advisor) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2014
Description
The Visceral Leishmaniasis (VL) is primarily endemic in five countries, with India and Sudan having the highest burden. The risk factors associated with VL are either unknown in some regions or vary drastically among empirical studies. Here, a dynamical model, motivated and informed by field data from the literature, is analyzed and employed to identify and quantify the impact of region dependent risks on the VL transmission dynamics. Parameter estimation procedures were developed using model-derived quantities and empirical data from multiple resources. The dynamics of VL depend on the estimates of the control reproductive number, RC, interpreted as the average number of secondary infections generated by a single infectious individual during the infectious period. The distribution of RC was estimated for both India (with mean 2.1 ± 1.1) and Sudan (with mean 1.45 ± 0.57). This suggests that VL can be established in naive regions of India more easily than in naive regions of Sudan. The parameter sensitivity analysis on RC suggests that the average biting rate and transmission probabilities between host and vector are among the most sensitive parameters for both countries. The comparative assessment of VL transmission dynamics in both India and Sudan was carried out by parameter sensitivity analysis on VL-related prevalences (such as prevalences of asymptomatic hosts, symptomatic hosts, and infected vectors). The results identify that the treatment and symptoms’ developmental rates are parameters that are highly sensitive to VL symptomatic and asymptomatic host prevalence, respectively, for both countries. It is found that the estimates of transmission probability are significantly different between India (from human to sandflies with mean of 0.39 ± 0.12; from sandflies to human with mean 0.0005 ± 0.0002) and Sudan (from human to sandflies with mean 0.26 ± 0.07; from sandflies to human with mean 0.0002 ± 0.0001). The results have significant implications for elimination. An increasing focus on elimination requires a review of priorities within the VL control agenda. The development of systematic implementation of control programs based on identified risk factors (such as monitoring of asymptomatically infected individuals) has a high transmission-blocking potential.
ContributorsBarley, Kamal K (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Safan, Muntaser (Committee member) / Arizona State University (Publisher)
Created2016