Biomedical subjects

Linda J S Allen

Publications and source records attributed to Linda J S Allen.

9 recordsLinked to original sources

PubMed2006

Disease emergence in multi-host epidemic models.

Most pathogens are capable of infecting multiple hosts. These multiple hosts provide many avenues for the disease to emerge. In this investigation, we formulate and analyse multi-host epidemic models and determine conditions under which the disease can emerge. In particular, SIS and SIR epidemic models are formulated for a pathogen that can infect n different hosts. The basic reproduction number is computed and shown to increase with n, the number of hosts that can be infected. Therefore, the possibility of disease emergence increases with the number of hosts infected. The SIS model for two hosts is studied in detail. Necessary and sufficient conditions are derived for the global stability of an endemic equilibrium. Numerical examples illustrate the dynamics of the two- and three-host epidemic models. The models have applications to hantavirus in rodents and other zoonotic diseases with multiple hosts.

Algorithms↗

PubMed2006

Mathematical models for hantavirus infection in rodents.

Hantavirus pulmonary syndrome is an emerging disease of humans that is carried by wild rodents. Humans are usually exposed to the virus through geographically isolated outbreaks. The driving forces behind these outbreaks is poorly understood. Certainly, one key driver of the emergence of these viruses is the virus population dynamics within the rodent population. Two new mathematical models for hantavirus infection in rodents are formulated and studied. The new models include the dynamics of susceptible, exposed, infective, and recovered male and female rodents. The first model is a system of ordinary differential equations while the second model is a system of stochastic differential equations. These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels.

Algorithms↗

PubMed2005

A spatially structured metapopulation model with patch dynamics.

Metapopulation models that incorporate both spatial and temporal structure are studied in this paper. The existence and stability of equilibria are provided, and an extinction threshold condition is derived which depends on patch dynamics (patch destruction and creation) and metapopulation dynamics (patch colonization and extinction). These results refine threshold conditions given by previous metapopulation models. By comparing landscapes with different spatial heterogeneities with respect to weighted long-term patch occupancies, we conclude that the pattern of a landscape is of overwhelming importance in determining metapopulation persistence and patch occupancy. We show that the same conclusion holds when a rescue effect is considered. We also derive a stochastic differential equations (SDE) model of the Itô type based on our deterministic model. Our simulations reveal good agreement between the deterministic model and the SDE model.

Animals↗

PubMed2005

A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability.

A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.

Animals↗

PubMed2004

Coexistence of multiple pathogen strains in stochastic epidemic models with density-dependent mortality.

Stochastic differential equations that model an SIS epidemic with multiple pathogen strains are derived from a system of ordinary differential equations. The stochastic model assumes there is demographic variability. The dynamics of the deterministic model are summarized. Then the dynamics of the stochastic model are compared to the deterministic model. In the deterministic model, there can be either disease extinction, competitive exclusion, where only one strain persists, or coexistence, where more than one strain persists. In the stochastic model, all strains are eventually eliminated because the disease-free state is an absorbing state. However, if the population size and the initial number of infected individuals are sufficiently large, it may take a long time until all strains are eliminated. Numerical simulations of the stochastic model show that coexistence cases predicted by the deterministic model are an unlikely occurrence in the stochastic model even for short time periods. In the stochastic model, either disease extinction or competitive exclusion occur. The initial number of infected individuals, the basic reproduction numbers, and other epidemiological parameters are important determinants of the dominant strain in the stochastic epidemic model.

Communicable Diseases↗

PubMed2003

Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size.

We study an SIR epidemic model with a variable host population size. We prove that if the model parameters satisfy certain inequalities then competition between n pathogens for a single host leads to exclusion of all pathogens except the one with the largest basic reproduction number. It is shown that a knowledge of the basic reproduction numbers is necessary but not sufficient for determining competitive exclusion. Numerical results illustrate that these inequalities are sufficient but not necessary for competitive exclusion to occur. In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur.

Algorithms↗

PubMed2003

The dynamics of two viral infections in a single host population with applications to hantavirus.

An SI epidemic model for a host with two viral infections circulating within the population is developed, analyzed, and numerically simulated. The model is a system of four differential equations which includes a state for susceptible individuals, two states for individuals infected with a single virus, one which is vertically transmitted and the other which is horizontally transmitted, and a fourth state for individuals infected with both viruses. A general growth function with density-dependent mortality is assumed. A special case of this model, where there is no coinfection and total cross immunity, is thoroughly analyzed. Several threshold values are defined which determine establishment of the disease and persistence at equilibrium for one or both of the infections within the host population. The model has applications to a hantavirus and an arenavirus that infect cotton rats. The hantavirus is transmitted horizontally whereas the arenavirus is transmitted vertically. It is shown through analysis and numerical simulations that both diseases can be maintained within a single host population, where individuals can be either infected with both viruses or with a single virus.

Animals↗

PubMed2003

A comparison of three different stochastic population models with regard to persistence time.

Results are summarized from the literature on three commonly used stochastic population models with regard to persistence time. In addition, several new results are introduced to clearly illustrate similarities between the models. Specifically, the relations between the mean persistence time and higher-order moments for discrete-time Markov chain models, continuous-time Markov chain models, and stochastic differential equation models are compared for populations experiencing demographic variability. Similarities between the models are demonstrated analytically, and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models are consistently formulated. As an example, the three stochastic models are applied to a population satisfying logistic growth. Logistic growth is interesting as different birth and death rates can yield the same logistic differential equation. However, the persistence behavior of the population is strongly dependent on the explicit forms for the birth and death rates. Computational results demonstrate how dramatically the mean persistence time can vary for different populations that experience the same logistic growth.

Animals↗

PubMedDate not supplied

Genetic models for plant pathosystems.

Deterministic, discrete time, genetics models for a resistant plant host and a virulent pathogen are developed and analyzed. The original model was developed by Leonard in 1977 for a single gene with haploid pathogens and diploid hosts [Ann. N.Y. Acad. Sci. 287 (1977) 207]. The original model is generalized to diploid hosts and pathogens with incomplete dominance of the heterozygote. In addition, the single gene model is extended to two genes and a stochastic model with random selection values is formulated and simulated. It is shown using local stability properties that stability of the polymorphic equilibrium is indeterminant; the equilibrium is non-hyperbolic. The original model of Leonard has this same property. However, with random selection values, solutions tend to converge toward the polymorphic equilibrium.

Models, Genetic↗