Infectious Disease and Species Coexistence: A Model of Lotka-Volterra Form

Holt, Robert D.; Pickering, John

doi:10.1086/284409

Cited by 262 publications

(220 citation statements)

References 32 publications

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“…where κ is the carrying capacity, b i is the rate of recruitment of species i, and all trees are assumed to exhibit equivalent competitive effects irrespective of species or disease status (Holt and Pickering, 1985;Preedy et al, 2007;Borer et al, 2007). However, the results of the optimization problem remain unchanged for the use of more complex growth functions such a logistic function.…”

Section: The Modelmentioning

confidence: 99%

Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission

Ndeffo-Mbah¹,

Gilligan²

2010

Journal of Theoretical Biology

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There is growing interest in incorporating economic factors into epidemiological models in order to identify optimal strategies for disease control when resources are limited. In this paper we consider how to optimize the control of a pathogen that is capable of infecting multiple hosts with different rates of transmission within and between species. Our objective is to find control strategies that maximize the discounted number of healthy individuals. We consider two classes of host-pathogen system, comprising two host species and a common pathogen, one with asymmetrical and the other with symmetrical transmission rates, applicable to a wide range of SI (susceptible-infected) epidemics of plant and animal pathogens. We motivate the analyses with an example of sudden oak death in California coastal forests, caused by Phytophthora ramorum, in communities dominated by bay laurel (Umbellularia californica) and tanoak (Lithocarpus densiflorus). We show for the asymmetric case that it is optimal to give priority in treating disease to the more infectious species, and to treat the other species only when there are resources left over. For the symmetric case, we show that although a switching strategy is an optimum, in which preference is first given to the species with the lower level of susceptibles and then to the species with the higher level of susceptibles, a simpler strategy that favours treatment of infected hosts for the more susceptible species is a robust alternative for practical application when the optimal switching time is unknown. Finally, since transmission rates are notoriously difficult to estimate, we analyze the robustness of the strategies when the true state with respect to symmetry or otherwise is unknown but one or other is assumed.

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Section: The Modelmentioning

confidence: 99%

Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission

Ndeffo-Mbah¹,

Gilligan²

2010

Journal of Theoretical Biology

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“…These theoretical models deal mainly with simple systems involving a parasite (a microparasite or a macroparasite, as defined in Anderson & May (1979)) infecting one host species. Few models deal with three species interactions, such as a parasite infecting two competitors, one predator and one prey, or other similar complex systems (May & Hassell 1981;Holt & Pickering 1985;Hochberg & Holt 1990;Begon et al 1992). However, host species, or even individuals, are usually not infected by just a single parasite species, but rather by a whole parasite community (review in Combes 1995).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of two feline retroviruses (FIV and FeLV) within one population of cats

Courchamp

Suppo

Fromont

et al. 1997

Proc. R. Soc. Lond. B

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We present a deterministic model of the dynamics of two microparasites simultaneously infecting a single host population. Both microparasites are feline retroviruses, namely Feline Immunodeficiency Virus (FIV) and Feline Leukaemia Virus (FeLV). The host is the domestic cat Felis catus. The model has been tested with data generated by a long-term study of several natural cat populations. Stability analysis and simulations show that, once introduced in a population, FIV spreads and is maintained, while FeLV can either disappear or persist. Moreover, introduction of both viruses into the population induces an equilibrium state for individuals of each different pathological class. The viruses never induce the extinction of the population. Furthermore, whatever the outcome for the host population (persistence of FIV only, or of both viruses), the global population size at the equilibrium state is only slightly lower than it would have been in the absence of the infections (i.e. at the carrying capacity), indicating a low impact of the viruses on the population. Finally, the impact of the diseases examined simultaneously is higher than the sum of the impact of the two diseases examined separately. This seems to be due to a higher mortality rate when both viruses infect a single individual.

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“…While few explicit models of this idea exist (Brown et al, 2006;Tompkins et al, 2003), one can trace the genesis of the idea to early work on apparent competition. In the first model of apparent competition in a host-microparasite system, Holt and Pickering (1985) found that in the presence of a parasite that infects two distinct populations, the population with relatively low resistance would be displaced by the more resistant population. In the model we present here, we show the more general result that any non-parasitized population can be displaced, even if it has higher resistance than invading parasitized population.…”

Section: Invasion Analysismentioning

confidence: 99%

“…Both theoretical models and empirical studies suggest that parasites can significantly alter, and in some cases reverse, the dynamics of both direct (Greenman and Hudson, 1999;Kiesecker and Blaustein, 1999;Park, 1948;Schall, 1992) and indirect competition (Bonsall and Hassell, 1997;Holt, 1977;Holt and Pickering, 1985;Settle and Wilson, 1990;Tompkins et al, 2001). Furthermore, from an applied perspective, parasites may threaten native biodiversity by affecting the dynamics of interspecific competition and therefore facilitate ecological invasions (Bedhomme et al, 2005;Prenter et al, 2004;Torchin et al, 2002).…”

Section: Introductionmentioning

confidence: 99%

The unavoidable costs and unexpected benefits of parasitism: Population and metapopulation models of parasite-mediated competition

Kuo

Corby‐Harris

Promislow

2008

Journal of Theoretical Biology

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When faced with limited resources, organisms have to determine how to allocate their resources to maximize fitness. In the presence of parasites, hosts may be selected for their ability to balance between the two competing needs of reproduction and immunity. These decisions can have consequences not only for host fitness, but also for the ability of parasites to persist within the population, and for the competitive dynamics between different host species. We develop two mathematical models to investigate how resource allocation strategies evolve at both population and metapopulation levels. The evolutionarily stable strategy (ESS) at the population level is a balanced investment between reproduction and immunity that maintains parasites, even though the host has the capacity to eliminate parasites. The host exhibiting the ESS can always invade other host populations through parasite-mediated competition, effectively using the parasites as biological weapons. At the metapopulation level, the dominant strategy is sometimes different from the population-level ESS, and depends on the ratio of local extinction rate to host colonization rate. This study may help to explain why parasites are as common as they are, and can serve as a modeling framework for investigating parasite-mediated ecological invasions. Furthermore, this work highlights the possibility that the 'introduction of enemies' process may facilitate species invasion.

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Infectious Disease and Species Coexistence: A Model of Lotka-Volterra Form

Cited by 262 publications

References 32 publications

Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission

Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission

Dynamics of two feline retroviruses (FIV and FeLV) within one population of cats

The unavoidable costs and unexpected benefits of parasitism: Population and metapopulation models of parasite-mediated competition

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