Matching Items (52)
Description
Diseases have been part of human life for generations and evolve within the population, sometimes dying out while other times becoming endemic or the cause of recurrent outbreaks. The long term influence of a disease stems from different dynamics within or between pathogen-host, that have been analyzed and studied by many researchers using mathematical models. Co-infection with different pathogens is common, yet little is known about how infection with one pathogen affects the host's immunological response to another. Moreover, no work has been found in the literature that considers the variability of the host immune health or that examines a disease at the population level and its corresponding interconnectedness with the host immune system. Knowing that the spread of the disease in the population starts at the individual level, this thesis explores how variability in immune system response within an endemic environment affects an individual's vulnerability, and how prone it is to co-infections. Immunology-based models of Malaria and Tuberculosis (TB) are constructed by extending and modifying existing mathematical models in the literature. The two are then combined to give a single nine-variable model of co-infection with Malaria and TB. Because these models are difficult to gain any insight analytically due to the large number of parameters, a phenomenological model of co-infection is proposed with subsystems corresponding to the individual immunology-based model of a single infection. Within this phenomenological model, the variability of the host immune health is also incorporated through three different pathogen response curves using nonlinear bounded Michaelis-Menten functions that describe the level or state of immune system (healthy, moderate and severely compromised). The immunology-based models of Malaria and TB give numerical results that agree with the biological observations. The Malaria--TB co-infection model gives reasonable results and these suggest that the order in which the two diseases are introduced have an impact on the behavior of both. The subsystems of the phenomenological models that correspond to a single infection (either of Malaria or TB) mimic much of the observed behavior of the immunology-based counterpart and can demonstrate different behavior depending on the chosen pathogen response curve. In addition, varying some of the parameters and initial conditions in the phenomenological model yields a range of topologically different mathematical behaviors, which suggests that this behavior may be able to be observed in the immunology-based models as well. The phenomenological models clearly replicate the qualitative behavior of primary and secondary infection as well as co-infection. The mathematical solutions of the models correspond to the fundamental states described by immunologists: virgin state, immune state and tolerance state. The phenomenological model of co-infection also demonstrates a range of parameter values and initial conditions in which the introduction of a second disease causes both diseases to grow without bound even though those same parameters and initial conditions did not yield unbounded growth in the corresponding subsystems. This results applies to all three states of the host immune system. In terms of the immunology-based system, this would suggest the following: there may be parameter values and initial conditions in which a person can clear Malaria or TB (separately) from their system but in which the presence of both can result in the person dying of one of the diseases. Finally, this thesis studies links between epidemiology (population level) and immunology in an effort to assess the impact of pathogen's spread within the population on the immune response of individuals. Models of Malaria and TB are proposed that incorporate the immune system of the host into a mathematical model of an epidemic at the population level.
ContributorsSoho, Edmé L (Author) / Wirkus, Stephen (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2011
Description
In an effort to address the lack of literature in on-campus active travel, this study aims to investigate the following primary questions:<br/>• What are the modes that students use to travel on campus?<br/>• What are the motivations that underlie the mode choice of students on campus?<br/>My first stage of research involved a series of qualitative investigations. I held one-on-one virtual interviews with students in which I asked them questions about the mode they use and why they feel that their chosen mode works best for them. These interviews served two functions. First, they provided me with insight into the various motivations underlying student mode choice. Second, they provided me with an indication of what explanatory variables should be included in a model of mode choice on campus.<br/>The first half of the research project informed a quantitative survey that was released via the Honors Digest to attract student respondents. Data was gathered on travel behavior as well as relevant explanatory variables.<br/>My analysis involved developing a logit model to predict student mode choice on campus and presenting the model estimation in conjunction with a discussion of student travel motivations based on the qualitative interviews. I use this information to make a recommendation on how campus infrastructure could be modified to better support the needs of the student population.
ContributorsMirtich, Laura Christine (Author) / Salon, Deborah (Thesis director) / Fang, Kevin (Committee member) / School of Public Affairs (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.
ContributorsVega-Guzmán, José Manuel, 1982- (Author) / Sulov, Sergei K (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Platte, Rodrigo (Committee member) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2013
Description
Mortality of 1918 influenza virus was high, partly due to bacteria coinfections. We characterize pandemic mortality in Arizona, which had high prevalence of tuberculosis. We applied regressions to over 35,000 data points to estimate the basic reproduction number and excess mortality. Age-specific mortality curves show elevated mortality for all age groups, especially the young, and senior sparing effects. The low value for reproduction number indicates that transmissibility was moderately low.
ContributorsJenner, Melinda Eva (Author) / Chowell-Puente, Gerardo (Thesis director) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
Background: While research has quantified the mortality burden of the 1957 H2N2 influenza pandemic in the United States, little is known about how the virus spread locally in Arizona, an area where the dry climate was promoted as reducing respiratory illness transmission yet tuberculosis prevalence was high.
Methods: Using archival death certificates from 1954 to 1961, this study quantified the age-specific seasonal patterns, excess-mortality rates, and transmissibility patterns of the 1957 pandemic in Maricopa County, Arizona. By applying cyclical Serfling linear regression models to weekly mortality rates, the excess-mortality rates due to respiratory and all-causes were estimated for each age group during the pandemic period. The reproduction number was quantified from weekly data using a simple growth rate method and generation intervals of 3 and 4 days. Local newspaper articles from The Arizona Republic were analyzed from 1957-1958.
Results: Excess-mortality rates varied between waves, age groups, and causes of death, but overall remained low. From October 1959-June 1960, the most severe wave of the pandemic, the absolute excess-mortality rate based on respiratory deaths per 10,000 population was 17.85 in the elderly (≥65 years). All other age groups had extremely low excess-mortality and the typical U-shaped age-pattern was absent. However, relative risk was greatest (3.61) among children and young adolescents (5-14 years) from October 1957-March 1958, based on incidence rates of respiratory deaths. Transmissibility was greatest during the same 1957-1958 period, when the mean reproduction number was 1.08-1.11, assuming 3 or 4 day generation intervals and exponential or fixed distributions.
Conclusions: Maricopa County largely avoided pandemic influenza from 1957-1961. Understanding this historical pandemic and the absence of high excess-mortality rates and transmissibility in Maricopa County may help public health officials prepare for and mitigate future outbreaks of influenza.
Methods: Using archival death certificates from 1954 to 1961, this study quantified the age-specific seasonal patterns, excess-mortality rates, and transmissibility patterns of the 1957 pandemic in Maricopa County, Arizona. By applying cyclical Serfling linear regression models to weekly mortality rates, the excess-mortality rates due to respiratory and all-causes were estimated for each age group during the pandemic period. The reproduction number was quantified from weekly data using a simple growth rate method and generation intervals of 3 and 4 days. Local newspaper articles from The Arizona Republic were analyzed from 1957-1958.
Results: Excess-mortality rates varied between waves, age groups, and causes of death, but overall remained low. From October 1959-June 1960, the most severe wave of the pandemic, the absolute excess-mortality rate based on respiratory deaths per 10,000 population was 17.85 in the elderly (≥65 years). All other age groups had extremely low excess-mortality and the typical U-shaped age-pattern was absent. However, relative risk was greatest (3.61) among children and young adolescents (5-14 years) from October 1957-March 1958, based on incidence rates of respiratory deaths. Transmissibility was greatest during the same 1957-1958 period, when the mean reproduction number was 1.08-1.11, assuming 3 or 4 day generation intervals and exponential or fixed distributions.
Conclusions: Maricopa County largely avoided pandemic influenza from 1957-1961. Understanding this historical pandemic and the absence of high excess-mortality rates and transmissibility in Maricopa County may help public health officials prepare for and mitigate future outbreaks of influenza.
ContributorsCobos, April J (Author) / Jehn, Megan (Thesis director) / Chowell-Puente, Gerardo (Committee member) / Barrett, The Honors College (Contributor) / School of Human Evolution and Social Change (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
Mathematical epidemiology, one of the oldest and richest areas in mathematical biology, has significantly enhanced our understanding of how pathogens emerge, evolve, and spread. Classical epidemiological models, the standard for predicting and managing the spread of infectious disease, assume that contacts between susceptible and infectious individuals depend on their relative frequency in the population. The behavioral factors that underpin contact rates are not generally addressed. There is, however, an emerging a class of models that addresses the feedbacks between infectious disease dynamics and the behavioral decisions driving host contact. Referred to as “economic epidemiology” or “epidemiological economics,” the approach explores the determinants of decisions about the number and type of contacts made by individuals, using insights and methods from economics. We show how the approach has the potential both to improve predictions of the course of infectious disease, and to support development of novel approaches to infectious disease management.
ContributorsPerrings, Charles (Author) / Castillo-Chavez, Carlos (Author) / Chowell-Puente, Gerardo (Author) / Daszak, Peter (Author) / Fenichel, Eli P. (Author) / Finnoff, David (Author) / Horan, Richard D. (Author) / Kilpatrick, A. Marm (Author) / Kinzig, Ann (Author) / Kuminoff, Nicolai (Author) / Levin, Simon (Author) / Morin, Benjamin (Author) / Smith, Katherine F. (Author) / Springborn, Michael (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / W.P. Carey School of Business (Contributor) / Economics (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor)
Created2015-12-01
Description
Background
In the weeks following the first imported case of Ebola in the U. S. on September 29, 2014, coverage of the very limited outbreak dominated the news media, in a manner quite disproportionate to the actual threat to national public health; by the end of October, 2014, there were only four laboratory confirmed cases of Ebola in the entire nation. Public interest in these events was high, as reflected in the millions of Ebola-related Internet searches and tweets performed in the month following the first confirmed case. Use of trending Internet searches and tweets has been proposed in the past for real-time prediction of outbreaks (a field referred to as “digital epidemiology”), but accounting for the biases of public panic has been problematic. In the case of the limited U. S. Ebola outbreak, we know that the Ebola-related searches and tweets originating the U. S. during the outbreak were due only to public interest or panic, providing an unprecedented means to determine how these dynamics affect such data, and how news media may be driving these trends.
Methodology
We examine daily Ebola-related Internet search and Twitter data in the U. S. during the six week period ending Oct 31, 2014. TV news coverage data were obtained from the daily number of Ebola-related news videos appearing on two major news networks. We fit the parameters of a mathematical contagion model to the data to determine if the news coverage was a significant factor in the temporal patterns in Ebola-related Internet and Twitter data.
Conclusions
We find significant evidence of contagion, with each Ebola-related news video inspiring tens of thousands of Ebola-related tweets and Internet searches. Between 65% to 76% of the variance in all samples is described by the news media contagion model.
In the weeks following the first imported case of Ebola in the U. S. on September 29, 2014, coverage of the very limited outbreak dominated the news media, in a manner quite disproportionate to the actual threat to national public health; by the end of October, 2014, there were only four laboratory confirmed cases of Ebola in the entire nation. Public interest in these events was high, as reflected in the millions of Ebola-related Internet searches and tweets performed in the month following the first confirmed case. Use of trending Internet searches and tweets has been proposed in the past for real-time prediction of outbreaks (a field referred to as “digital epidemiology”), but accounting for the biases of public panic has been problematic. In the case of the limited U. S. Ebola outbreak, we know that the Ebola-related searches and tweets originating the U. S. during the outbreak were due only to public interest or panic, providing an unprecedented means to determine how these dynamics affect such data, and how news media may be driving these trends.
Methodology
We examine daily Ebola-related Internet search and Twitter data in the U. S. during the six week period ending Oct 31, 2014. TV news coverage data were obtained from the daily number of Ebola-related news videos appearing on two major news networks. We fit the parameters of a mathematical contagion model to the data to determine if the news coverage was a significant factor in the temporal patterns in Ebola-related Internet and Twitter data.
Conclusions
We find significant evidence of contagion, with each Ebola-related news video inspiring tens of thousands of Ebola-related tweets and Internet searches. Between 65% to 76% of the variance in all samples is described by the news media contagion model.
ContributorsTowers, Sherry (Author) / Afzal, Shehzad (Author) / Bernal, Gilbert (Author) / Bliss, Nadya (Author) / Brown, Shala (Author) / Espinoza, Baltazar (Author) / Jackson, Jasmine (Author) / Judson-Garcia, Julia (Author) / Khan, Maryam (Author) / Lin, Michael (Author) / Mamada, Robert (Author) / Moreno, Victor (Author) / Nazari, Fereshteh (Author) / Okuneye, Kamaldeen (Author) / Ross, Mary (Author) / Rodriguez, Claudia (Author) / Medlock, Jan (Author) / Ebert, David (Author) / Castillo-Chavez, Carlos (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / Mary Lou Fulton Teachers College (Contributor) / Educational Leadership and Innovation (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Global Security Initiative (Contributor)
Created2015-06-11
Description
Background
Seroepidemiological studies before and after the epidemic wave of H1N1-2009 are useful for estimating population attack rates with a potential to validate early estimates of the reproduction number, R, in modeling studies.
Methodology/Principal Findings
Since the final epidemic size, the proportion of individuals in a population who become infected during an epidemic, is not the result of a binomial sampling process because infection events are not independent of each other, we propose the use of an asymptotic distribution of the final size to compute approximate 95% confidence intervals of the observed final size. This allows the comparison of the observed final sizes against predictions based on the modeling study (R = 1.15, 1.40 and 1.90), which also yields simple formulae for determining sample sizes for future seroepidemiological studies. We examine a total of eleven published seroepidemiological studies of H1N1-2009 that took place after observing the peak incidence in a number of countries. Observed seropositive proportions in six studies appear to be smaller than that predicted from R = 1.40; four of the six studies sampled serum less than one month after the reported peak incidence. The comparison of the observed final sizes against R = 1.15 and 1.90 reveals that all eleven studies appear not to be significantly deviating from the prediction with R = 1.15, but final sizes in nine studies indicate overestimation if the value R = 1.90 is used.
Conclusions
Sample sizes of published seroepidemiological studies were too small to assess the validity of model predictions except when R = 1.90 was used. We recommend the use of the proposed approach in determining the sample size of post-epidemic seroepidemiological studies, calculating the 95% confidence interval of observed final size, and conducting relevant hypothesis testing instead of the use of methods that rely on a binomial proportion.
Seroepidemiological studies before and after the epidemic wave of H1N1-2009 are useful for estimating population attack rates with a potential to validate early estimates of the reproduction number, R, in modeling studies.
Methodology/Principal Findings
Since the final epidemic size, the proportion of individuals in a population who become infected during an epidemic, is not the result of a binomial sampling process because infection events are not independent of each other, we propose the use of an asymptotic distribution of the final size to compute approximate 95% confidence intervals of the observed final size. This allows the comparison of the observed final sizes against predictions based on the modeling study (R = 1.15, 1.40 and 1.90), which also yields simple formulae for determining sample sizes for future seroepidemiological studies. We examine a total of eleven published seroepidemiological studies of H1N1-2009 that took place after observing the peak incidence in a number of countries. Observed seropositive proportions in six studies appear to be smaller than that predicted from R = 1.40; four of the six studies sampled serum less than one month after the reported peak incidence. The comparison of the observed final sizes against R = 1.15 and 1.90 reveals that all eleven studies appear not to be significantly deviating from the prediction with R = 1.15, but final sizes in nine studies indicate overestimation if the value R = 1.90 is used.
Conclusions
Sample sizes of published seroepidemiological studies were too small to assess the validity of model predictions except when R = 1.90 was used. We recommend the use of the proposed approach in determining the sample size of post-epidemic seroepidemiological studies, calculating the 95% confidence interval of observed final size, and conducting relevant hypothesis testing instead of the use of methods that rely on a binomial proportion.
ContributorsNishiura, Hiroshi (Author) / Chowell-Puente, Gerardo (Author) / Castillo-Chavez, Carlos (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2011-03-24
Description
Background
Several past studies have found that media reports of suicides and homicides appear to subsequently increase the incidence of similar events in the community, apparently due to the coverage planting the seeds of ideation in at-risk individuals to commit similar acts.
Methods
Here we explore whether or not contagion is evident in more high-profile incidents, such as school shootings and mass killings (incidents with four or more people killed). We fit a contagion model to recent data sets related to such incidents in the US, with terms that take into account the fact that a school shooting or mass murder may temporarily increase the probability of a similar event in the immediate future, by assuming an exponential decay in contagiousness after an event.
Conclusions
We find significant evidence that mass killings involving firearms are incented by similar events in the immediate past. On average, this temporary increase in probability lasts 13 days, and each incident incites at least 0.30 new incidents (p = 0.0015). We also find significant evidence of contagion in school shootings, for which an incident is contagious for an average of 13 days, and incites an average of at least 0.22 new incidents (p = 0.0001). All p-values are assessed based on a likelihood ratio test comparing the likelihood of a contagion model to that of a null model with no contagion. On average, mass killings involving firearms occur approximately every two weeks in the US, while school shootings occur on average monthly. We find that state prevalence of firearm ownership is significantly associated with the state incidence of mass killings with firearms, school shootings, and mass shootings.
Several past studies have found that media reports of suicides and homicides appear to subsequently increase the incidence of similar events in the community, apparently due to the coverage planting the seeds of ideation in at-risk individuals to commit similar acts.
Methods
Here we explore whether or not contagion is evident in more high-profile incidents, such as school shootings and mass killings (incidents with four or more people killed). We fit a contagion model to recent data sets related to such incidents in the US, with terms that take into account the fact that a school shooting or mass murder may temporarily increase the probability of a similar event in the immediate future, by assuming an exponential decay in contagiousness after an event.
Conclusions
We find significant evidence that mass killings involving firearms are incented by similar events in the immediate past. On average, this temporary increase in probability lasts 13 days, and each incident incites at least 0.30 new incidents (p = 0.0015). We also find significant evidence of contagion in school shootings, for which an incident is contagious for an average of 13 days, and incites an average of at least 0.22 new incidents (p = 0.0001). All p-values are assessed based on a likelihood ratio test comparing the likelihood of a contagion model to that of a null model with no contagion. On average, mass killings involving firearms occur approximately every two weeks in the US, while school shootings occur on average monthly. We find that state prevalence of firearm ownership is significantly associated with the state incidence of mass killings with firearms, school shootings, and mass shootings.
ContributorsTowers, Sherry (Author) / Gomez-Lievano, Andres (Author) / Khan, Maryam (Author) / Mubayi, Anuj (Author) / Castillo-Chavez, Carlos (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2015-07-02
Description
Traditional Reinforcement Learning (RL) assumes to learn policies with respect to reward available from the environment but sometimes learning in a complex domain requires wisdom which comes from a wide range of experience. In behavior based robotics, it is observed that a complex behavior can be described by a combination of simpler behaviors. It is tempting to apply similar idea such that simpler behaviors can be combined in a meaningful way to tailor the complex combination. Such an approach would enable faster learning and modular design of behaviors. Complex behaviors can be combined with other behaviors to create even more advanced behaviors resulting in a rich set of possibilities. Similar to RL, combined behavior can keep evolving by interacting with the environment. The requirement of this method is to specify a reasonable set of simple behaviors. In this research, I present an algorithm that aims at combining behavior such that the resulting behavior has characteristics of each individual behavior. This approach has been inspired by behavior based robotics, such as the subsumption architecture and motor schema-based design. The combination algorithm outputs n weights to combine behaviors linearly. The weights are state dependent and change dynamically at every step in an episode. This idea is tested on discrete and continuous environments like OpenAI’s “Lunar Lander” and “Biped Walker”. Results are compared with related domains like Multi-objective RL, Hierarchical RL, Transfer learning, and basic RL. It is observed that the combination of behaviors is a novel way of learning which helps the agent achieve required characteristics. A combination is learned for a given state and so the agent is able to learn faster in an efficient manner compared to other similar approaches. Agent beautifully demonstrates characteristics of multiple behaviors which helps the agent to learn and adapt to the environment. Future directions are also suggested as possible extensions to this research.
ContributorsVora, Kevin Jatin (Author) / Zhang, Yu (Thesis advisor) / Yang, Yezhou (Committee member) / Praharaj, Sarbeswar (Committee member) / Arizona State University (Publisher)
Created2021