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.

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.

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 (R_0) 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.