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- All Subjects: Epidemiology
- Creators: Kang, Yun
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
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
In this dissertation the potential impact of some social, cultural and economic factors on
Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability
to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is
addressed. A mathematical model, calibrated with data from the 2014 West African outbreak,
is used to show the dynamics of EVD control under various quarantine and isolation
effectiveness regimes. It is shown that in order to make a difference it must reach a high
proportion of the infected population. The effect of EVD-dead bodies has been incorporated
in the quarantine effectiveness. In Chapter four, the potential impact of differential
risk is assessed. A two-patch model without explicitly incorporate quarantine is used to
assess the impact of mobility on communities at risk of EVD. It is shown that the
overall EVD burden may lessen when mobility in this artificial high-low risk society is allowed.
The cost that individuals in the low-risk patch must pay, as measured by secondary
cases is highlighted. In Chapter five a model explicitly incorporating patch-specific quarantine
levels is used to show that quarantine a large enough proportion of the population
under effective isolation leads to a measurable reduction of secondary cases in the presence
of mobility. It is shown that sharing limited resources can improve the effectiveness of
EVD effective control in the two-patch high-low risk system. Identifying the conditions
under which the low-risk community would be willing to accept the increases in EVD risk,
needed to reduce the total number of secondary cases in a community composed of two
patches with highly differentiated risks has not been addressed. In summary, this dissertation
looks at EVD dynamics within an idealized highly polarized world where resources
are primarily in the hands of a low-risk community – a community of lower density, higher
levels of education and reasonable health services – that shares a “border” with a high-risk
community that lacks minimal resources to survive an EVD outbreak.
Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability
to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is
addressed. A mathematical model, calibrated with data from the 2014 West African outbreak,
is used to show the dynamics of EVD control under various quarantine and isolation
effectiveness regimes. It is shown that in order to make a difference it must reach a high
proportion of the infected population. The effect of EVD-dead bodies has been incorporated
in the quarantine effectiveness. In Chapter four, the potential impact of differential
risk is assessed. A two-patch model without explicitly incorporate quarantine is used to
assess the impact of mobility on communities at risk of EVD. It is shown that the
overall EVD burden may lessen when mobility in this artificial high-low risk society is allowed.
The cost that individuals in the low-risk patch must pay, as measured by secondary
cases is highlighted. In Chapter five a model explicitly incorporating patch-specific quarantine
levels is used to show that quarantine a large enough proportion of the population
under effective isolation leads to a measurable reduction of secondary cases in the presence
of mobility. It is shown that sharing limited resources can improve the effectiveness of
EVD effective control in the two-patch high-low risk system. Identifying the conditions
under which the low-risk community would be willing to accept the increases in EVD risk,
needed to reduce the total number of secondary cases in a community composed of two
patches with highly differentiated risks has not been addressed. In summary, this dissertation
looks at EVD dynamics within an idealized highly polarized world where resources
are primarily in the hands of a low-risk community – a community of lower density, higher
levels of education and reasonable health services – that shares a “border” with a high-risk
community that lacks minimal resources to survive an EVD outbreak.
ContributorsEspinoza Cortes, Baltazar (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Kang, Yun (Committee member) / Safan, Muntaser (Committee member) / Arizona State University (Publisher)
Created2018
Description
Unlike the autosomes, recombination on the sex chromosomes is limited to the pseudoautosomal regions (PARs) at each end of the chromosome. PAR1 spans approximately 2.7 Mb from the tip of the proximal arm of each sex chromosome, and a pseudoautosomal boundary between the PAR1 and non-PAR region is thought to have evolved from a Y-specific inversion that suppressed recombination across the boundary. In addition to the two PARs, there is also a human-specific X-transposed region (XTR) that was duplicated from the X to the Y chromosome. Genetic diversity is expected to be higher in recombining than nonrecombining regions, particularly because recombination reduces the effects of linked selection, allowing neutral variation to accumulate. We previously showed that diversity decreases linearly across the previously defined pseudoautosomal boundary (rather than drop suddenly at the boundary), suggesting that the pseudoautosomal boundary may not be as strict as previously thought. In this study, we analyzed data from 1271 genetic females to explore the extent to which the pseudoautosomal boundary varies among human populations (broadly, African, European, South Asian, East Asian, and the Americas). We found that, in all populations, genetic diversity was significantly higher in the PAR1 and XTR than in the non-PAR regions, and that diversity decreased linearly from the PAR1 to finally reach a non-PAR value well past the pseudoautosomal boundary in all populations. However, we also found that the location at which diversity changes from reflecting the higher PAR1 diversity to the lower nonPAR diversity varied by as much as 500 kb among populations. The lack of genetic evidence for a strict pseudoautosomal boundary and the variability in patterns of diversity across the pseudoautosomal boundary are consistent with two potential explanations: (1) the boundary itself may vary across populations, or (2) that population-specific demographic histories have shaped diversity across the pseudoautosomal boundary.
ContributorsCotter, Daniel Juetten (Author) / Wilson Sayres, Melissa (Thesis director) / Stone, Anne (Committee member) / Webster, Timothy (Committee member) / School of Life Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
This work examines one dimension of the effect that complex human transport systems have on the spread of Chikungunya Virus (CHIKV) in the Caribbean from 2013 to 2015. CHIKV is transmitted by mosquitos and its novel spread through the Caribbean islands provided a chance to examine disease transmission through complex human transportation systems. Previous work by Cauchemez et al. had shown a simple distance-based model successfully predict CHIKV spread in the Caribbean using Markov chain Monte Carlo (MCMC) statistical methods. A MCMC simulation is used to evaluate different transportation methods (air travel, cruise ships, and local maritime traffic) for the primary transmission patterns through linear regression. Other metrics including population density to account for island size variation and dengue fever incidence rates as a proxy for vector control and health spending were included. Air travel and cruise travel were gathered from monthly passenger arrivals by island. Local maritime traffic is approximated with a gravity model proxy incorporating GDP-per-capita and distance and historic dengue rates were used for determine existing vector control measures for the islands. The Caribbean represents the largest cruise passenger market in the world, cruise ship arrivals were expected to show the strongest signal; however, the gravity model representing local traffic was the best predictor of infection routes. The early infected islands (<30 days) showed a heavy trend towards an alternate primary transmission but our consensus model able to predict the time until initial infection reporting with 94.5% accuracy for islands 30 days post initial reporting. This result can assist public health entities in enacting measures to mitigate future epidemics and provide a modelling basis for determining transmission modes in future CHIKV outbreaks.
ContributorsFries, Brendan F (Author) / Perrings, Charles (Thesis director) / Wilson Sayres, Melissa (Committee member) / Morin, Ben (Committee member) / School of Life Sciences (Contributor) / Department of Military Science (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
Description
A pneumonia-like illness emerged late in 2019 (coined COVID-19), caused by SARSCoV-2, causing a devastating global pandemic on a scale never before seen sincethe 1918/1919 influenza pandemic. This dissertation contributes in providing deeper
qualitative insights into the transmission dynamics and control of the disease in the
United States. A basic mathematical model, which incorporates the key pertinent
epidemiological features of SARS-CoV-2 and fitted using observed COVID-19 data,
was designed and used to assess the population-level impacts of vaccination and face
mask usage in mitigating the burden of the pandemic in the United States. Conditions
for the existence and asymptotic stability of the various equilibria of the model were
derived. The model was shown to undergo a vaccine-induced backward bifurcation
when the associated reproduction number is less than one. Conditions for achieving
vaccine-derived herd immunity were derived for three of the four FDA-approved vaccines (namely Pfizer, Moderna and Johnson & Johnson vaccine), and the vaccination
coverage level needed to achieve it decreases with increasing coverage of moderately and highly-effective face masks. It was also shown that using face masks as a singular
intervention strategy could lead to the elimination of the pandemic if moderate or
highly-effective masks are prioritized and pandemic elimination prospects are greatly
enhanced if the vaccination program is combined with a face mask use strategy that
emphasizes the use of moderate to highly-effective masks with at least moderate coverage. The model was extended in Chapter 3 to allow for the assessment of the
impacts of waning and boosting of vaccine-derived and natural immunity against
the BA.1 Omicron variant of SARS-CoV-2. It was shown that vaccine-derived herd
immunity can be achieved in the United States via a vaccination-boosting strategy
which entails fully vaccinating at least 72% of the susceptible populace. Boosting
of vaccine-derived immunity was shown to be more beneficial than boosting of natural immunity. Overall, this study showed that the prospects of the elimination of
the pandemic in the United States were highly promising using the two intervention
measures.
ContributorsSafdar, Salman (Author) / Gumel, Abba (Thesis advisor) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Fricks, John (Committee member) / Espanol, Malena (Committee member) / Arizona State University (Publisher)
Created2023