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EPIDEMIOLOGICAL MODELS FOR MUTATING PATHOGENS WITH TEMPORARY IMMUNITY
Title
EPIDEMIOLOGICAL MODELS FOR MUTATING PATHOGENS WITH TEMPORARY IMMUNITY.
Creator
Singh, Neeta, Rollins, David, University of Central Florida
Abstract / Description
Significant progress has been made in understanding different scenarios for disease transmissions and behavior of epidemics in recent years. A considerable amount of work has been done in modeling the dynamics of diseases by systems of ordinary differential equations. But there are very few mathematical models that deal with the genetic mutations of a pathogen. In-fact, not much has been done to model the dynamics of mutations of pathogen explaining its effort to escape the host's immune...
Show moreSignificant progress has been made in understanding different scenarios for disease transmissions and behavior of epidemics in recent years. A considerable amount of work has been done in modeling the dynamics of diseases by systems of ordinary differential equations. But there are very few mathematical models that deal with the genetic mutations of a pathogen. In-fact, not much has been done to model the dynamics of mutations of pathogen explaining its effort to escape the host's immune defense system after it has infected the host. In this dissertation we develop an SIR model with variable infection age for the transmission of a pathogen that can mutate in the host to produce a second infectious mutant strain. We assume that there is a period of temporary immunity in the model. A temporary immunity period along with variable infection age leads to an integro-differential-difference model. Previous efforts on incorporating delays in epidemic models have mainly concentrated on inclusion of latency periods (this assumes that the force of infection at a present time is determined by the number of infectives in the past). We begin with reviewing some basic models. These basic models are the building blocks for the later, more detailed models. Next we consider the model for mutation of pathogen and discuss its implications. Finally, we improve this model for mutation of pathogen by incorporating delay induced by temporary immunity. We examine the influence of delay as we establish the existence, and derive the explicit forms of disease-free, boundary and endemic equilibriums. We will also investigate the local stability of each of these equilibriums. The possibility of Hopf bifurcation using delay as the bifurcation parameter is studied using both analytical and numerical solutions.
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Date Issued
2006
Identifier
CFE0001043, ucf:46801
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001043
A mathematical model for feral cat ecology with application to disease.
Title
A mathematical model for feral cat ecology with application to disease.
Creator
Sharpe, Jeff, Nevai, A, Shuai, Zhisheng, Qi, Yuanwei, Quintana-Ascencio, Pedro, University of Central Florida
Abstract / Description
We formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to Lotka-Volterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also...
Show moreWe formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to Lotka-Volterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also considered, including additional competition and abandonment into the feral population. Control measures are also modeled in the form of per-capita removal rates. We compute the net reproduction number (R_0) for the colony and consider its influence. In the absence of abandonment, if R_0(>)1, the population always persists at a positive equilibrium and if R_0 (<)= 1, the population always tends toward local extinction. This work will be referred to as the core model.The model is then expanded to include a set of colonies (patches) such as those in the core model (this time neglecting the effect of abandonment). Adult females and kittens remain in their native patch while adult males spend a fixed proportion of their time in each patch. Adult females experience competition from both the adult females living in the same patch as well as the visiting adult males. The proportion of adult males in patch j suffer competition from both adult females resident to that patch as well the proportion of adult males also in the patch. We formulate a net reproduction number for each patch (a patch reproduction number) R_j. If R_j(>)1 for at least one patch, then the collective population always persists at some nontrivial (but possibly semitrivial) steady state. We consider the number of possible steady states and their properties. This work will be referred to as the patch model.Finally, the core model is expanded to include the introduction of the feline leukemia virus. Since this disease has many modes of transmission, each of which depends on the host's gender and life-stage, we regard this as a model disease. A basic reproduction number R_0 for the disease is defined and analyzed. Vaccination terms are included and their role in disease propagation is analyzed. Necessary and sufficient conditions are given under which the disease-free equilibrium is stable.
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Date Issued
2016
Identifier
CFE0006502, ucf:51389
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0006502