PubMed Health⌕ Search

Biomedical subjects

J A Heesterbeek

Publications and source records attributed to J A Heesterbeek.

11 recordsLinked to original sources
PubMed2000

On optimal size and number of reserves for metapopulation persistence.

Habitat fragmentation is generally considered to be detrimental to the persistence of natural populations. In nature management, one therefore tends to prefer few large nature reserves over many small nature reserves having equal total area. This paper examines whether this preference is warranted in a metapopulation framework with circular reserves (patches) by formulating the dependence of metapopulation persistence on the size and number of reserves, both of which depend on reserve radius if the total area is kept constant. Two measures of metapopulation persistence are used: R(0), the number of patches colonized by an occupied patch during its lifetime as an occupied patch, and T(e), the expected time to extinction. These two measures are functions of the extinction and colonization rates of the metapopulation. Several mechanisms for the extinction and colonization processes are formulated from which the dependence of these rates on reserve radius is calculated. It turns out that T(e)generally increases with reserve radius for all mechanisms, which supports the preference of few large reserves. However, R(0)supports this preference only in the case of some special, rather unrealistic, mechanisms. In many other, more realistic, cases an intermediate reserve size exists for which metapopulation persistence measured by R(0)is optimal.

Animals↗
PubMed1998

A simple parasite model with complicated dynamics.

During their first year of life sheep acquire parasites through grazing, and simultaneously build up an immunity to infection. At the beginning of each year non-immune lambs are introduced onto contaminated pasture. We represent this process by differential equations describing the within-year dynamics, and defining a difference equation that describes the between-year dynamics. An example with two system parameters is analysed in detail. It is shown that regions exist in parameter space where periodic (between-year) or aperiodic solutions occur. Parasite control schemes could change the system dynamics from a stable equilibrium to complicated long-term fluctuations.

Animals↗
PubMed1996

Vector-borne diseases and the basic reproduction number: a case study of African horse sickness.

The basic reproduction number, R0, can be used to determine factors important in the ability of a disease to invade or persist. We show how this number can be derived or estimated for vector-borne diseases with different complicating factors. African horse sickness is a viral disease transmitted mainly by the midge Culicoides imicola. We use this as an example of such a vector-transmitted disease where latent periods, seasonality in vector populations, and multiple host types may be important. The effect of vector population dynamics which are dependent on either host or vector density are also addressed. If density-dependent constraints on vector population density are less severe, R0 is more sensitive to vector mortality and the virus development rate. Host-dependent vector dynamics change the relationship between R0 and host population size. Seasonality can either increase or decrease the estimate of R0, depending on the lag between the peak of the midge population and the infective host population. The relative abundance of two host types is a factor in the ability of a disease to invade, but the strength of this factor depends on the differences between the hosts in recovery from infection, mortality and transmission. Removal of a reservoir host may increase R0.

African Horse Sickness↗
PubMed1995

Threshold quantities for helminth infections.

For parasites with a clearly defined life-cycle we give threshold quantities that determine the stability of the parasite-free steady state for autonomous and periodic deterministic systems formulated in terms of mean parasite burdens. We discuss the biological interpretations of the quantities, how to deal with heterogeneity in both parasite and host populations, how to incorporate the effects of periodic discontinuities, and the relation of the threshold quantities to the basic reproduction ratio Ro. Examples from the literature are given. The analysis of the periodic case extends easily to 'micro-parasitic' systems.

Animals↗
PubMed1995

The dynamics of nematode infections of farmed ruminants.

In this paper the dynamics and control of nematode parasites of farmed ruminants are discussed via a qualitative analysis of a differential equation model. To achieve this a quantity, 'the basic reproduction quotient' (Q0), whose definition coincides with previous definitions of R0 for macroparasites, but extends to models with periodic time-varying transition rates between parasite stages or management interventions, is introduced. This quantity has the usual threshold property: if Q0 is less than one the parasite population cannot maintain itself in the host population, and in the long term becomes extinct; but if Q0 is greater than one the parasite can invade the host population. An alternative quantity, R(E), that is often easier to calculate is also introduced, and shown to have the same threshold property. The use of these two quantities in analysing models for the dynamics of nematodes in complex situations is then demonstrated, with reference to the dynamics of mixed parasite species in one host; the effects of breeding host animals for resistance to parasitism; and the development of parasite strains that are resistant to chemotherapy. Five examples are discussed using parameters for the dynamics of nematode infections in sheep, and some statements on control policies are derived.

Animals↗
PubMed1994

The computation of R0 for discrete-time epidemic models with dynamic heterogeneity.

An explicit algorithm is given for the computation of the basic reproduction ratio R0 (or the net reproduction ratio R in the case of a not wholly susceptible population) for a class of discrete-time epidemic models. These models allow for a finite number of different individual types, type changes at fixed type-dependent intervals, arbitrary contact intensity between individuals of the various types, and variable infectivity. The models reflect the situation where an infectious disease spreads in a population of animals that are reared in different stables on farms. In addition, it is shown analytically that the reproduction ratio depends, for any given type, on the product of the susceptibility and the total infectivity of that type and not on these factors separately. We call this product the transmission weight of the type. The maximum overall transmission weight gives an upper bound for the reproduction ratio, irrespective of the particular submodels for type change and contact structure. Reduction of all transmission weights below 1, by vaccination or some other control measure, will result in R < 1 and will hence lead to eradication of the disease.

Algorithms↗
PubMed1993

The saturating contact rate in marriage- and epidemic models.

In this note we show how to derive, by a mechanistic argument, an expression for the saturating contact rate of individual contacts in a population that mixes randomly. The main assumption is that the individual interaction times are typically short as compared to the time-scale of changes in, for example, individual-type, but that the interactions yet make up a considerable fraction of the time-budget of an individual. In special cases an explicit formula for the contact rate is obtained. The result is applied to mathematical epidemiology and marriage models.

Acquired Immunodeficiency Syndrome↗
PubMed1990

On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations.

The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.

Age Factors↗
PubMed1989

How to estimate the efficacy of periodic control of an infectious plant disease.

Certain infectious plant diseases are controlled by inspection and subsequent hand removal of diseased parts. In this paper we give two sets of criteria from which one can conclude whether this control effort is adequate or not. These criteria do not require knowledge of the infection- or detection rate of the disease but only use the structure of the contact matrix. Computer experiments give a feeling of how many inspections are needed in order to draw a conclusion.

Epidemiologic Methods↗
PubMedDate not supplied

The basic reproduction ratio for sexually transmitted diseases. Part 2. Effects of variable HIV infectivity.

In this paper we investigate the effects of variable infectivity on the spread of HIV in a heterosexual population where pair formation and separation are taken into account. We calculate the basic reproduction ratio as a function of the number of new partners during the infectious period, keeping the total number of contacts fixed. Numerical evidence suggests that the basic reproduction ratio decreases for variable infectivity if the average infectivity is kept constant.

Acquired Immunodeficiency Syndrome↗