Interacting populations : hosts and pathogens, prey and predators

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2007The interactions between populations can be positive, neutral or negative. Predation and parasitism are both relationships where one species benefits from the interaction at the expense of the other. Predators kill their prey instantly and use it only for food, whereas parasites use their hosts both as their habitat and their food. I am particularly interested in microbial parasites (including bacteria, fungi, viri, and some protozoans) since they cause many infectious diseases. This thesis considers two different points in the population-interaction spectrum and focuses on modeling host-pathogen and predator-prey interactions. The first part focuses on epidemiology, i. e., the dynamics of infectious diseases, and the estimation of parameters using the epidemiological data from two different diseases, phocine distemper virus that affects harbor seals in Europe, and the outbreak of HIV/AIDS in Cuba. The second part analyzes the stability of the predator-prey populations that are spatially organized into discrete units or patches. Patches are connected by dispersing individuals that may, or may not differ in the duration of their trip. This travel time is incorporated via a dispersal delay in the interpatch migration term, and has a stabilizing effect on predator-prey dynamics.This work has been supported by the US National Science Foundation (DEB-0235692), the US Environmental Protection Agency (R-82908901), the Ocean Ventures Fund, and the Academic Programs Office

2010 Conference Abstracts: Annual Undergraduate Research Conference at the Interface of Biology and Mathematics

Abstract book for the Second Annual Undergraduate Research Conference at the Interface of Biology and Mathematics Date: November 19 - 20, 2010Plenary speaker: Abdul-Aziz Yakubu, Professor and Chair of the Department of Mathematics, Howard UniversityFeatured speaker: Jory Weintraub, Assistant Director Education and Outreach, National Evolutionary Synthesis Cente

A Systematic Review of Mathematical Models of Dengue Transmission and Vector Control: 2010–2020

Vector control methods are considered effective in averting dengue transmission. However, several factors may modify their impact. Of these controls, chemical methods, in the long run, may increase mosquitoes’ resistance to chemicides, thereby decreasing control efficacy. The biological methods, which may be self-sustaining and very effective, could be hampered by seasonality or heatwaves (resulting in, e.g., loss of Wolbachia infection). The environmental methods that could be more effective than the chemical methods are under-investigated. In this study, a systematic review is conducted to explore the present understanding of the effectiveness of vector control approaches via dengue transmission models

Global dynamics of some vector-borne infectious disease models with seasonality

Vector-borne infectious diseases such as malaria, dengue, West Nile fever, Zika fever and Lyme disease remain a threat to public health and economics. Both vector life cycle and parasite development are greatly influenced by climatic factors. Understanding the role of seasonal climate in vector-borne infectious disease transmission is particularly important in light of global warming. This PhD thesis is devoted to the study of global dynamics of four vector-borne infectious disease models. We start with a periodic vector-bias malaria model with constant extrinsic incubation period (EIP). To explore the temperature sensitivity of the EIP of malaria parasites, we also formulate a functional differential equations model with a periodic time delay. Moreover, we incorporate the use of insecticide-treated bed nets (ITNs) into a climate-based mosquito-stage-structured malaria model. Lastly, we develop a time-delayed Lyme disease model with seasonality. By using the theory of basic reproduction ratio, R0, and the theory of dynamical systems, we derive R0 and establish a threshold type result for the global dynamics in terms of R0 for each model. By conducting numerical simulations of case studies, we propose some practical strategies for the control of the diseases

Construction and analysis of efficient numerical methods to solve mathematical models of TB and HIV co-infection

Philosophiae Doctor - PhDThe global impact of the converging dual epidemics of tuberculosis (TB) and human immunodeficiency virus (HIV) is one of the major public health challenges of our time, because in many countries, human immunodeficiency virus (HIV) and mycobacterium tuberculosis (TB) are among the leading causes of morbidity and mortality. It is found that infection with HIV increases the risk of reactivating latent TB infection, and HIV-infected individuals who acquire new TB infections have high rates of disease progression. Research has shown that these two diseases are enormous public health burden, and unfortunately, not much has been done in terms of modeling the dynamics of HIV-TB co-infection at a population level. In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models. Comparative numerical results are also provided for each model.South Afric