Matching Items (13)
Description
This dissertation examines six different models in the field of econophysics using interacting particle systems as the basis of exploration. In each model examined, the underlying structure is a graph G = (V , E ), where each x ∈ V represents an individual who is characterized by the number of coins in her possession at time t. At each time step t, an edge (x, y) ∈ E is chosen at random, resulting in an exchange of coins between individuals x and y according to the rules of the model. Random variables ξt, and ξt(x) keep track of the current configuration and number of coins individual x has at time t respectively. Of particular interest is the distribution of coins in the long run. Considered first are the uniform reshuffling model, immediate exchange model and model with saving propensity. For each of these models, the number of coins an individual can have is nonnegative and the total number of coins in the system is conserved for all time. It is shown here that the distribution of coins converges to the exponential distribution, gamma distribution and a pseudo gamma distribution respectively. The next two models introduce debt, however, the total number of coins again remains fixed. It is shown here that when there is an individual debt limit, the number of coins per individual converges to a shifted exponential distribution. Alternatively, when a collective debt limit is imposed on the whole population, a heuristic argument is given supporting the conjecture that the distribution of coins converges to an asymmetric Laplace distribution. The final model considered focuses on the effect of cooperation on a population. Unlike the previous models discussed here, the total number of coins in the system at any given time is not bounded and the process evolves in continuous time rather than in discrete time. For this model, death of an individual will occur if they run out of coins. It is shown here that the survival probability for the population is impacted by the level of cooperation along with how productive the population is as whole.
ContributorsReed, Stephanie Jo (Author) / Lanchier, Nicolas (Thesis advisor) / Smith, Hal (Committee member) / Gumel, Abba (Committee member) / Motsch, Sebastien (Committee member) / Camacho, Erika (Committee member) / Arizona State University (Publisher)
Created2019
Description
In recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic Lotka-Volterra model with n + 1 bacteria, n
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.
It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.
Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model
of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton
acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.
It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.
Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model
of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton
acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
ContributorsKorytowski, Daniel (Author) / Smith, Hal (Thesis advisor) / Gumel, Abba (Committee member) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2016
Description
The Kingdom of Saudi Arabia (KSA), which hosts some of the largest mass gatherings of humans globally every year, has seen the emergence of two coronavirus pandemics, namely the 2012 middle eastern respiratory syndrome (MERS-CoV) and the 2019 SARS-CoV-2 pandemics. This dissertation contributes in providing deeper insight into the transmission dynamics and control of the two diseases in the Kingdom. A model for SARS-CoV-2 transmission dynamics, which incorporates the key features of the disease, was designed first of all. Its disease-free equilibrium was shown, using Lyapunov function theory, to be globally-asymptotically stable when the associated reproduction number is less than one. The model, which has a unique and locally-asymptotically stable endemic equilibrium (for a special case) when the reproduction threshold exceeds one, was fitted using observed data for the KSA. Global sensitivity analysis was carried out to identify the key parameters of the model that have the most influence on the disease burden in the Kingdom. The model was used to assess the population-level impacts of control and mitigation interventions. It was shown that a face mask use strategy, based on using masks of moderate to high efficacy, can lead to the elimination of the pandemic if the coverage in its usage is high enough. A model for the spread of MERS-CoV in the human and camel host populations was also designed, rigorously analysed, and fitted with data. The model was later extended to include the use of intervention measures, notably vaccination of humans and camels and the use of face mask by humans in public or when having frequent closed contacts with camels. The population-level impacts of these interventions, implemented in isolation or in combinations, were assessed. The study showed that focusing intervention resources on containing the MERS-CoV spread in the camel population would be more effective than on containing the spread in humans.
ContributorsAlatawi, Adel (Author) / Gumel, Abba (Thesis advisor) / Arizona State University (Publisher)
Created2023
Description
\begin{abstract}The human immunodeficiency virus (HIV) pandemic, which causes the syndrome of opportunistic infections that characterize the late stage HIV disease, known as the acquired immunodeficiency syndrome (AIDS), remains a major public health challenge to many parts of the world. This dissertation contributes in providing deeper qualitative insights into the transmission dynamics and control of the HIV/AIDS disease in Men who have Sex with Men (MSM) community. A new mathematical model (which is relatively basic), which incorporates some of the pertinent aspects of HIV epidemiology and immunology and fitted using the yearly new case data of the MSM population from the State of Arizona, was designed and used to assess the population-level impact of awareness of HIV infection status and condom-based intervention, on the transmission dynamics and control of HIV/AIDS in an MSM community. Conditions for the existence and asymptotic stability of the various equilibria ofthe model were derived. The numerical simulations showed that the prospects for the effective control and/or elimination of HIV/AIDS in the MSM community in the United States are very promising using a condom-based intervention, provided the condom efficacy is high and the compliance is moderate enough. The model was extended in Chapter 3 to account for the effect of risk-structure, staged-progression property of HIV disease, and the use of pre-exposure prophylaxis (PrEP) on the spread and control of the disease. The model was shown to undergo a PrEP-induced \textit{backward bifurcation} when the associated control reproduction number is less than one. It was shown that when the compliance in PrEP usage is $50%(80%)$ then about $19.1%(34.2%)$ of the yearly new HIV/AIDS cases recorded at the peak will have been prevented, in comparison to the worst-case scenario where PrEP-based intervention is not implemented in the MSM community. It was also shown that the HIV pandemic elimination is possible from the MSM community even for the scenario when the effective contact rate is increased by 5-fold from its baseline value, if low-risk individuals take at least 15 years before they change their risky behavior and transition to the high-risk group (regardless of the value of the transition rate from high-risk to low-risk susceptible population).
ContributorsTollett, Queen Wiggs (Author) / Gumel, Abba (Thesis advisor) / Crook, Sharon (Committee member) / Fricks, John (Committee member) / Gardner, Carl (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2023
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
Description
Since its isolation from a rhesus monkey in the Zika forest of Uganda in 1947, Zika virus (ZIKV) has spread into many parts of the world, causing major epidemics, notably in the Americas and some parts of Europe and Asia. The flavivirus ZIKV is primarily transmitted to humans via the bite of infectious adult female Aedes mosquitoes. In the absence of effective treatment or a safe and effective vaccine against the disease, control efforts are focused on effective vector management to reduce the mosquito population and limit human exposure to mosquito bites. The work in this thesis is based on the use of a mathematical model for gaining insight into the transmission dynamics of ZIKV in a population. The model, which takes the form of a deterministic system of nonlinear differential equations, is rigorously analyzed to gain insight into its basic qualitative features. In particular, it is shown that the disease-free equilibrium of the model is locally-asymptotically stable whenever a certain epidemiological quantity (known as the reproduction number, denoted by R0) is less than unity. The epidemiological implication of this result is that a small influx of ZIKV-infected individuals or vectors into the community will not generate a large outbreak if the anti-ZIKV control strategy (or strategies) adopted by the community can reduce and maintain R0 to a value less than unity. Numerical simulations of the model, using data relevant to ZIKV transmission dynamics in Puerto Rico, shows that a control strategy that solely focuses on killing immature mosquitoes (using highly efficacious larvicides) can lead to the elimination of ZIKV if the larvicide coverage (i.e., proportion of breeding sites treated with larvicides) is high enough (over 90%). Such elimination is also feasible using a control strategy that solely focuses on the use of insect repellents (as a means of personal protection against mosquito bites) if the coverage level of the insect repellent usage in the community is high enough (at least 70%). However, it is also shown that although the use of adulticides (i.e., using insecticides to kill adult mosquitoes) can reduce the reproduction number (hence, disease burden), it fails to reduce it to a value less than unity, regardless of coverage level. Thus, unlike with the use of larvicide-only or repellent-only strategies, the population-wide implementation of an adulticide-only strategy is unable to lead to ZIKV elimination. Finally, it is shown that the combined (integrated pest management) strategy, based on using all three aforementioned strategies, is the most effective approach for combatting ZIKV in the population. In particular, it is shown that even a moderately-effective level of this strategy, which entails using only 50% coverage of both larvicides and adulticides, together with about 45% coverage for a repellent strategy, will lead to ZIKV elimination. This moderately-effective combined strategy seems attainable in Puerto Rico.
ContributorsUrcuyo, Javier (Author) / Gumel, Abba (Thesis director) / Hackney Price, Jennifer (Committee member) / School of Mathematical and Natural Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Background: Ebola is one of the most virulent human viral diseases, with a case fatality ratio between 25% to 90%. The 2014 West African outbreaks are the largest and worst in history. There is no specific treatment or effective/safe vaccine against the disease. Hence, control efforts are restricted to basic public health preventive (non-pharmaceutical) measures. Such efforts are undermined by traditional/cultural belief systems and customs, characterized by general mistrust and skepticism against government efforts to combat the disease. This study assesses the roles of traditional customs and public healthcare systems on the disease spread.
Methods: A mathematical model is designed and used to assess population-level impact of basic non-pharmaceutical control measures on the 2014 Ebola outbreaks. The model incorporates the effects of traditional belief systems and customs, along with disease transmission within health-care settings and by Ebola-deceased individuals. A sensitivity analysis is performed to determine model parameters that most affect disease transmission. The model is parameterized using data from Guinea, one of the three Ebola-stricken countries. Numerical simulations are performed and the parameters that drive disease transmission, with or without basic public health control measures, determined. Three effectiveness levels of such basic measures are considered.
Results: The distribution of the basic reproduction number (R0) for Guinea (in the absence of basic control measures) is such that R 0 ∈ [0.77,1.35], for the case when the belief systems do not result in more unreported Ebola cases. When such systems inhibit control efforts, the distribution increases to R 0 ∈ [1.15,2.05]. The total Ebola cases are contributed by Ebola-deceased individuals (22%), symptomatic individuals in the early (33%) and latter (45%) infection stages. A significant reduction of new Ebola cases can be achieved by increasing health-care workers’ daily shifts from 8 to 24 hours, limiting hospital visitation to 1 hour and educating the populace to abandon detrimental traditional/cultural belief systems.
Conclusions: The 2014 outbreaks are controllable using a moderately-effective basic public health intervention strategy alone. A much higher (>50%) disease burden would have been recorded in the absence of such intervention.
ContributorsAgusto, Folashade B. (Author) / Teboh-Ewungkem, Miranda I. (Author) / Gumel, Abba (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2015-04-23
Description
Although extracellular throughout their lifecycle, trypanosomes are able to persist despite strong host immune responses through a process known as antigenic variation involving a large, highly diverse family of surface glycopro- tein (VSG) genes, only one of which is expressed at a time. Previous studies have used mathematical models to investigate the relationship between VSG switching and the dynamics of trypanosome infections, but none have explored the role of multiple VSG expression sites or the contribution of mosaic gene conversion events involving VSG pseudogenes.
ContributorsKoury, Michael Andrew (Author) / Taylor, Jesse (Thesis director) / Gumel, Abba (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Malaria is a deadly, infectious, parasitic disease which is caused by Plasmodium parasites and transmitted between humans via the bite of adult female Anopheles mosquitoes. The primary insecticide-based interventions used to control malaria are indoor residual spraying (IRS) and long-lasting insecticide nets (LLINs). Larvicides are another insecticide-based intervention which is less commonly used. In this study, a mathematical model for malaria transmission dynamics in an endemic region which incorporates the use of IRS, LLINS, and larvicides is presented. The model is rigorously analyzed to gain insight into the asymptotic stability of the disease-free equilibrium. Simulations of the model show that individual insecticide-based interventions will not realistically control malaria in regions with high endemicity, but an integrated vector management strategy involving the use of multiple interventions could lead to the effective control of the disease. This study suggests that the use of larvicides alongside IRS and LLINs in endemic regions may be more effective than using only IRS and LLINs.
ContributorsJameson, Leah (Author) / Gumel, Abba (Thesis director) / Huijben, Silvie (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Civic & Economic Thought and Leadership (Contributor)
Created2022-05
Description
Dengue is a mosquito-borne arboviral disease that causes significant public health burden in many trophical and sub-tropical parts of the world (where dengue is endemic). This dissertation is based on using mathematical modeling approaches, coupled with rigorous analysis and computation, to study the transmission dynamics and control of dengue disease. In Chapter 2, a new deterministic model was designed and used to assess the impact of local fluctuation of temperature and mosquito vertical (transvasorial) transmission on the population abundance of dengue mosquitoes and disease in a population. The model, which takes the form of a deterministic system of nonlinear differential equations, was parametrized using data from the Chiang Mai province of Thailand. The disease-free equilibrium of the model was shown to be globally-asymptotically stable when a certain epidemiological quantity is less than unity. Vertical transmission was shown to only have marginal impact on the disease dynamics, and its effect is temperature-dependent. Dengue burden in the province is maximized when the mean monthly temperature lie in the range [26-28] C. A new deterministic model was designed in Chapter 3 to assess the impact of the release of Wolbachia-infected mosquitoes on curtailing the mosquito population and dengue disease in a population. The model, which stratifies the mosquito population in terms of sex and Wolbachia-infection status, was rigorously analysed to characterize the bifurcation property of the model as well as the asymptotic stability of the various disease-free equilibria. Simulations, using Wolbachia-based mosquito control from Queensland, Australia, showed that the frequent release of mosquitoes infected with the bacterium can lead to the effective control of the local wild mosquito population, and that such effective control increases with increasing number of Wolbachia-infected mosquitoes released (up to 90% reduction in the wild mosquito population, from their baseline values, can be achieved). It was also shown that the well-known feature of cytoplasmic incompatibility has very little effect on the effectiveness of the Wolbachia-based mosquito control.
ContributorsTaghikhani, Rahim (Author) / Gumel, Abba (Thesis advisor) / Crook, Sharon (Committee member) / Espanol, Malena (Committee member) / Kuang, Yang (Committee member) / Scotch, Matthew (Committee member) / Arizona State University (Publisher)
Created2020