On the Dynamics of Dengue Virus type 2 with Residence Times and Vertical Transmission

A two-patch mathematical model of Dengue virus type 2 (DENV-2) that accounts for vectors' vertical transmission and between patches human dispersal is introduced. Dispersal is modeled via a Lagrangian approach. A host-patch residence-times basic reproduction number is derived and conditions under which the disease dies out or persists are established. Analytical and numerical results highlight the role of hosts' dispersal in mitigating or exacerbating disease dynamics. The framework is used to explore dengue dynamics using, as a starting point, the 2002 outbreak in the state of Colima, Mexico

A Holistic Approach to Dynamic Modelling of Malaria Transmission. An Investigation of Climate-Based Models used for Predicting Malaria Transmission

The uninterrupted spread of malaria, besides its seasonal uncertainty, is due to the lack of suitable planning and intervention mechanisms and tools. Several studies have been carried out to understand the factors that affect the development and transmission of malaria, but these efforts have been largely limited to piecemeal specific methods, hence they do not offer comprehensive solutions to predict disease outbreaks. This thesis introduces a ’holistic’ approach to understand the relationship between climate parameters and the occurrence of malaria using both mathematical and computational methods. In this respect, we develop new climate-based models using mathematical, agent-based and data-driven modelling techniques. A malaria model is developed using mathematical modelling to investigate the impact of temperature-dependent delays. Although this method is widely applicable, but it is limited to the study of homogeneous populations. An agent-based technique is employed to address this limitation, where the spatial and temporal variability of agents involved in the transmission of malaria are taken into account. Moreover, whilst the mathematical and agent-based approaches allow for temperature and precipitation in the modelling process, they do not capture other dynamics that might potentially affect malaria. Hence, to accommodate the climatic predictors of malaria, an intelligent predictive model is developed using machine-learning algorithms, which supports predictions of endemics in certain geographical areas by monitoring the risk factors, e.g., temperature and humidity. The thesis not only synthesises mathematical and computational methods to better understand the disease dynamics and its transmission, but also provides healthcare providers and policy makers with better planning and intervention tools

Mathematical Modeling and Analysis of Epidemiological and Chemical Systems

This dissertation focuses on three interdisciplinary areas of applied mathematics, mathematical biology/epidemiology, economic epidemiology and mathematical physics, interconnected by the concepts and applications of dynamical systems.;In mathematical biology/epidemiology, a new deterministic SIS modeling framework for the dynamics of malaria transmission in which the malaria vector population is accounted for at each of its developmental stages is proposed. Rigorous qualitative and quantitative techniques are applied to acquire insights into the dynamics of the model and to identify and study two epidemiological threshold parameters reals* and R0 that characterize disease transmission and prevalence, and that can be used for disease control. It is shown that nontrivial disease-free and endemic equilibrium solutions, which can become unstable via a Hopf bifurcation exist. By incorporating vector demography; that is, by interpreting an aspect of the life cycle of the malaria vector, natural fluctuations known to exist in malaria prevalence are captured without recourse to external seasonal forcing and delays. Hence, an understanding of vector demography is necessary to explain the observed patterns in malaria prevalence. Additionally, the model exhibits a backward bifurcation. This implies that simply reducing R0 below unity may not be enough to eradicate the malaria disease. Since, only the female adult mosquitoes involved in disease transmission are identified and fully accounted for, the basic reproduction number (R0) for this model is smaller than that for previous SIS models for malaria. This, and the occurrence of both oscillatory dynamics and a backward bifurcation provide a novel and plausible framework for developing and implementing optimal malaria control strategies, especially those strategies that are associated with vector control.;In economic epidemiology, a deterministic and a stochastic model are used to investigate the effects of determinism, stochasticity, and safety nets on disease-driven poverty traps; that is, traps of low per capita income and high infectious disease prevalence. It is shown that economic development in deterministic models require significant external changes to the initial economic and health care conditions or a change in the parametric structure of the system. Therefore, poverty traps arising from deterministic models lead to more limited policy options. In contrast, there is always some probability that a population will escape or fall into a poverty trap in stochastic models. It is demonstrated that in stochastic models, a safety net can guarantee ultimate escape from the poverty trap, even when it is set within the basin of attraction of the poverty trap or when it is implemented only as an economic or health care intervention. It is also shown that the benefits of safety nets for populations that are close to the poverty trap equilibrium are highest for the stochastic model and lowest for the deterministic model. Based on the analysis of the stochastic model, the following optimal economic development and public health intervention questions are answered: (i) Is it preferable to provide health care, income/income generating resources, or both health care and income/income generating resources to enable populations to break cycles of poverty and disease; that is, escape from poverty traps? (ii) How long will it take a population that is caught in a poverty trap to attain economic development when the initial health and economic conditions are reinforced by safety nets?;In mathematical physics, an unusual form of multistability involving the coexistence of an infinite number of attractors that is exhibited by specially coupled chaotic systems is explored. It is shown that this behavior is associated with generalized synchronization and the emergence of a conserved quantity. The robustness of the phenomenon in relation to a mismatch of parameters of the coupled systems is studied, and it is shown that the special coupling scheme yields a new class of dynamical systems that manifests characteristics of dissipative and conservative systems

Mathematics of Climate Change and Mosquito-borne Disease Dynamics

abstract: The role of climate change, as measured in terms of changes in the climatology of geophysical variables (such as temperature and rainfall), on the global distribution and burden of vector-borne diseases (VBDs) remains a subject of considerable debate. This dissertation attempts to contribute to this debate via the use of mathematical (compartmental) modeling and statistical data analysis. In particular, the objective is to find suitable values and/or ranges of the climate variables considered (typically temperature and rainfall) for maximum vector abundance and consequently, maximum transmission intensity of the disease(s) they cause. Motivated by the fact that understanding the dynamics of disease vector is crucial to understanding the transmission and control of the VBDs they cause, a novel weather-driven deterministic model for the population biology of the mosquito is formulated and rigorously analyzed. Numerical simulations, using relevant weather and entomological data for Anopheles mosquito (the vector for malaria), show that maximum mosquito abundance occurs when temperature and rainfall values lie in the range [20-25]C and [105-115] mm, respectively. The Anopheles mosquito ecology model is extended to incorporate human dynamics. The resulting weather-driven malaria transmission model, which includes many of the key aspects of malaria (such as disease transmission by asymptomatically-infectious humans, and enhanced malaria immunity due to repeated exposure), was rigorously analyzed. The model which also incorporates the effect of diurnal temperature range (DTR) on malaria transmission dynamics shows that increasing DTR shifts the peak temperature value for malaria transmission from 29C (when DTR is 0C) to about 25C (when DTR is 15C). Finally, the malaria model is adapted and used to study the transmission dynamics of chikungunya, dengue and Zika, three diseases co-circulating in the Americas caused by the same vector (Aedes aegypti). The resulting model, which is fitted using data from Mexico, is used to assess a few hypotheses (such as those associated with the possible impact the newly-released dengue vaccine will have on Zika) and the impact of variability in climate variables on the dynamics of the three diseases. Suitable temperature and rainfall ranges for the maximum transmission intensity of the three diseases are obtained.Dissertation/ThesisDoctoral Dissertation Applied Mathematics 201

Effects of vector maturation time on the dynamics of cassava mosaic disease

Many plant diseases are caused by plant viruses that are often transmitted to plants by vectors. For instance, the cassava mosaic disease, which is spread by whiteflies, has a significant negative effect on plant growth and development. Since only mature whiteflies can contribute to the spread of the cassava mosaic virus, and the maturation time is non-negligible compared to whitefly lifetime, it is important to consider the effects this maturation time can have on the dynamics. In this paper, we propose a mathematical model for dynamics of cassava mosaic disease that includes immature and mature vectors and explicitly includes a time delay representing vector maturation time. A special feature of our plant epidemic model is that vector recruitment is negatively related to the delayed ratio between vector density and plant density. We identify conditions of biological feasibility and stability of different steady states in terms of system parameters and the time delay. Numerical stability analyses and simulations are performed to explore the role of various parameters, and to illustrate the behaviour of the model in different dynamical regimes. We show that the maturation delay may stabilise epidemiological dynamics that would otherwise be cyclic

Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various “Ross-Macdonald” mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955–1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention

Inferring Characteristics Of Malaria Infection Of Two Plasmodium Strains In Mice

Cerebral Malaria is a complex neurological condition that results from interaction between the host and the Plasmodium parasite through the different phases of parasite's life-cycle. This interaction ranges from infection to immune response triggered in the host system. Various strains of the Plasmodium parasites are found to have difference in the severity of disease after infection. However, the precise factors defining the infectivity of Plasmodium parasites and the resulting disease outcome have not been completely identified so far. In the thesis, the Plasmodium berghei mouse model for Malaria is used to characterize the infection dynamics of Plasmodium berghei ANKA (wild-type) and a mutant strain that lacks a Plasmodium antigen PbmaLS_05. The mutant infection leads to lower parasitemia in red blood cells and less severe disease outcome in contrast to mice infected with the wild-type strain. Moreover, the mice infected by injecting PbmaLS_05(-) KO-infected red blood cells show reduced immune response in contrast to infection with PbmaLS_05(-) KO-sporozoites. By developing mathematical models describing various mechanisms of the infection and fitting them to experimental data; I find factors that influence the difference in disease progression seen between the two strains. Most strikingly, the KO strain shows a decreased ability to infect immature red blood cells that are usually a preferred target of the parasite. This altered property of infection limits parasite burden and affects disease progression. In addition to this, a statistical analysis of immune activation and immune response data from the KO or WT infected mice was done, which resulted in selecting major indicators of cerebral Malaria. The analysis showed that the number of CD8+ T cells accumulated in the brain, the reduced proportion of CD8+ T cells to lymphocytes in the spleen, the increased presence of Malaria specific CD8+ IFN-+ T and the secondary activation of CD8+ T cells due to the antigens cross-presented by infected red blood cells sequestered in the brain are the prominent distinguishing factors between the ECM causing PbANKA and non-ECM causing PbmaLS_05 (-) infections. An exploratory analysis of the liver-stage of infection and immune response highlighted that PbmaLS_05 may not have an important role to play in triggered immune response during the liver-stage of Malaria. However, its absence may lead to a small decrease in number of productive infections during the liver-stage, which must be further investigated. The antigen PbmaLS_05 can potentially aid in discovering the factors that influence the activation of immune responses and that might contribute to vaccine development and efficient parasite control

The Population Biology and Transmission Dynamics of Loa loa

Endemic to Central Africa, loiasis – or African eye worm (caused by the filarial nematode Loa loa) – affects more than 10 million people. Despite causing ocular and systemic symptoms, it has typically been considered a benign condition, only of public health relevance because it impedes mass drug administration-based interventions against onchocerciasis and lymphatic filariasis in co-endemic areas. Recent research has challenged this conception, demonstrating excess mortality associated with high levels of infection, implying that loiasis warrants attention as an intrinsic public health problem. This review summarises available information on the key parasitological, entomological, and epidemiological characteristics of the infection and argues for the mobilisation of resources to control the disease, and the development of a mathematical transmission model to guide deployment of interventions