Regular articleA Model of Disease and Vaccination for Infections with Acute and Chronic Phases
Abstract
A general model is presented of a disease in which both recovered and vaccinated individuals are protected from acute disease, but are still susceptible to chronic infection. The special threshold conditions for the establishment and persistence of such a disease are derived and explained in full. The efficacies of alternative vaccination strategies are detailed and a specific example of such a disease is given by examining feline calicivirus (FCV), a cause of upper respiratory tract disease in cats.
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Can possible evolutionary outcomes be determined directly from the population dynamics?
2008, Theoretical Population BiologyTraditionally, to determine the possible evolutionary behaviour of an ecological system using adaptive dynamics, it is necessary to calculate the fitness and its derivatives at a singular point. We investigate the claim that the possible evolutionary behaviour can be predicted directly from the population dynamics, without the need for calculation, by applying three criteria — one based on the form of the density dependent rates and two on the role played by the evolving parameters. Taking a general continuous time model, with broad ecological range, we show that the claim is true. Initially, we assume that individuals enter in class 1 and move through population classes sequentially; later we relax these assumptions and find that the criteria still apply. However, when we consider models where the evolving parameters appear non-linearly in the dynamics, we find some aspects of the criteria fail; useful but weaker results on possible evolutionary behaviour now apply.
Global dynamics of an SEI model with acute and chronic stages
2008, Journal of Computational and Applied MathematicsA model with acute and chronic stages in a population with exponentially varying size is proposed. An equivalent system is obtained, which has two equilibriums: a disease-free equilibrium and an endemic equilibrium. The stability of these two equilibriums is controlled by the basic reproduction number . When , the disease-free equilibrium is globally stable. When , the disease-free equilibrium is unstable and the unique endemic equilibrium is locally stable. When and , the endemic equilibrium is globally stable in .
Calicivirus
2003, Antigenic VariationThe Caliciviridae is a family of small, nonenveloped, and icosahedral viruses. It has a positive sense, single-stranded RNA genome of approximately 7.5 kilobases. The Caliciviridae contains viruses responsible for a wide range of human and animal diseases. Subclassification of these viruses was difficult because of their inherent diversity and initial difficulties in characterizing a number of viruses that do not grow in cell culture. This chapter focuses on antigenic variations in feline caliciviruses (FCV). Feline caliciviruses were first identified in domestic cats in 1957. It is a relatively easy virus to study in the laboratory, unlike some other caliciviruses, as they grow readily in feline cell cultures. The pathogenesis of the FCV disease has been largely determined because feline infections can easily be established in specific pathogen-free cats under defined experimental conditions. There is a number of features of feline calicivirus that makes it an interesting pathogen in considering antigenic variations. First, FCV is an RNA virus that is likely to be prone to mutation and selection through a number of genetic mechanisms. Second, there is a wide spectrum of antigenic and genetic diversity in FCV, although this appears to be restricted within specific limits. Third, the virus is exceptionally successful in its host because of an asymptomatic carrier state that develops in a significant numbers of clinically recovered animals.
A model appropriate to the transmission of a human food-borne pathogen in a multigroup managed herd
2003, Preventive Veterinary MedicineWe describe a model of microparasite transmission within a multigroup managed farming system. The model was formulated to represent transmission of Escherichia coli O157 within a typical UK dairy herd and was used to suggest possible on-farm control strategies. The model includes birth, death, maturation, the dry/lactating cycle and various types of transmission (i.e. direct, pseudovertical (representing direct faecal–oral transmission between dam and calf within the first 48 h) and indirect (via free-living infectious units in the environment)). A combination of numerical and analytical techniques was used to analyse the model. We found that pseudovertical transmission and indirect transmission via infectious units in the ‘general’ environment can lead to more groups being affected, but otherwise have relatively little effect on the invasion criteria. To reduce infection within the herd, we suggest that efforts be directed at reducing the opportunity for group-specific indirect transmission—particularly within the weaned group.
Diseases with chronic stage in a population with varying size
2003, Mathematical BiosciencesAn epidemiological model of hepatitis C with a chronic infectious stage and variable population size is introduced. A non-structured baseline ODE model which supports exponential solutions is discussed. The normalized version where the unknown functions are the proportions of the susceptible, infected, and chronic individuals in the total population is analyzed. It is shown that sustained oscillations are not possible and the endemic proportions either approach the disease-free or an endemic equilibrium. The expanded model incorporates the chronic age of the individuals. Partial analysis of this age-structured model is carried out. The global asymptotic stability of the infection-free state is established as well as local asymptotic stability of the endemic non-uniform steady state distribution under some additional conditions. A numerical method for the chronic-age-structured model is introduced. It is shown that this numerical scheme is consistent and convergent of first order. Simulations based on the numerical method suggest that in the structured case the endemic equilibrium may be unstable and sustained oscillations are possible. Closer look at the reproduction number reveals that treatment strategies directed towards speeding up the transition from acute to chronic stage in effect contribute to the eradication of the disease.
Vaccination strategies and backward bifurcation in an age-since-infection structured model
2002, Mathematical BiosciencesWe consider models for a disease with acute and chronic infective stages, and variable infectivity and recovery rates, within the context of a vaccination campaign. Models for SIRS and SIS disease cycles exhibit backward bifurcations under certain conditions, which complicate the criteria for success of the vaccination campaign by making it possible to have stable endemic states when . We also show the extent to which the forms of the infectivity and recovery functions affect the possibility of backward bifurcations. SIR and SI models examined do not exhibit this behavior.
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