Population dynamics of fox rabies in Europe

Anderson, Roy M.; Jackson, Helen C.; May, Robert M.; Smith, Anthony M.

doi:10.1038/289765a0

Cited by 409 publications

(329 citation statements)

References 33 publications

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“…One of the most common mechanisms known to be capable of exciting oscillations derives from the return of infectives into a susceptible class (with or without having experienced a period of temporary immunity). Anderson et al (1981) found, for a fox rabies model, that sustained oscillations can be generated by the combined effects of a rapid turnover of the fox population and the relatively long latency and the high fatality of fox rabies. Liu et al (1986Liu et al ( , 1987, in their work on influenza, have shown that generalized nonlinear incidence rates can also generate sustained oscillations.…”

Section: Discussion and Projected Future Workmentioning

confidence: 99%

On the Role of Variable Infectivity in the Dynamics of the Human Immunodeficiency Virus Epidemic

Thieme

Castillo‐Chavez

1989

Lecture Notes in Biomathematics

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In this paper, we study the effects of variable infectivity in combination with a variable incubation period on the dynamics of HIV {the human immunodeficiency virus, the etiological agent for AIDS, the acquired immunodeficiency syndrome) in a homogeneously mixing population. In the model discussed here, the functional relationship between mean sexual activity and size of the population is assumed to be nonlinear and to saturate at high population sizes. We identify a basic reproductive number Ro and show that the disease dies out if R 0 < 1. If R 0 > 1 the incidence rate converges to or oscillates around a uniquely determined nonzero equilibrium, the stability of which is studied. Our findings provide the analytical basis for exploring the parameter range in which the equilibrium is locally asymptotically stable. Oscillations cannot be excluded in general, and may occur in particular, if the variable infectivity is concentrated at an earlier part of the incubation period. Whether they can also occur for the reported two peaks of infectivity observed in HIV-infected individuals has to be the subject of future numerical investigations.

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Section: Discussion and Projected Future Workmentioning

confidence: 99%

On the Role of Variable Infectivity in the Dynamics of the Human Immunodeficiency Virus Epidemic

Thieme

Castillo‐Chavez

1989

Lecture Notes in Biomathematics

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“…Mathematically, this can be understood by noting that both nullclines depend on μ, whereas only one nullcline depends on β, cf. Equation (4).…”

Section: Bifurcation Behaviourmentioning

confidence: 99%

“…There is a large body of evidence showing that disease agents can substantially affect their host population [4,28,37]. Besides causing a depression in population size, infectious diseases have also been attributed to playing a role in the extinction of species [13,14,30,50,54,60].…”

Section: Introductionmentioning

confidence: 99%

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect

Hilker

2010

Journal of Biological Dynamics

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Infectious diseases are responsible for the extinction of a number of species. In conventional epidemic models, the transition from endemic population persistence to extirpation takes place gradually. However, if host demographics exhibits a strong Allee effect (AE) (population decline at low densities), extinction can occur abruptly in a catastrophic population crash. This might explain why species suddenly disappear even when they used to persist at high endemic population levels. Mathematically, the tipping point towards population collapse is associated with a saddle-node bifurcation. The underlying mechanism is the simultaneous population size depression and the increase of the extinction threshold due to parasite pathogenicity and Allee effect. Since highly pathogenic parasites cause their own extinction but not that of their host, there can be another saddle-node bifurcation with the re-emergence of two endemic equilibria. The implications for control interventions are discussed, suggesting that effective management may be possible for R 0 1.

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“…In fact, varying total populations were discussed before (e.g. [1,3,5,9,11,22,29,36]). Here, we assume that the population of a community follows the logistic growth.…”

Section: Introductionmentioning

confidence: 99%

Media alert in an SIS epidemic model with logistic growth

Wang

Zhou

Liu

et al. 2016

Journal of Biological Dynamics

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In general, media coverage would not be implemented unless the number of infected cases reaches some critical number. To reflect this feature, we incorporate the media effect and a critical number of infected cases into the disease transmission rate and consider an susceptible-infected-susceptible epidemic model with logistic growth. Our model analysis shows that early media alert and strong media effects are preferable to decrease the numbers of infected cases at endemic equilibria. Furthermore, we noticed that the model may have up to three endemic equilibria and bi-stability can occur in a threshold interval for the critical number. Note that the interval depends on parameters for the focal disease and the media effect. It is possible to roughly estimate the interval for re-emerging diseases in a given region. Therefore, the result could be useful to health policymakers. Global stability is also obtained when the model admits a unique endemic equilibrium. ARTICLE HISTORY

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Population dynamics of fox rabies in Europe

Cited by 409 publications

References 33 publications

On the Role of Variable Infectivity in the Dynamics of the Human Immunodeficiency Virus Epidemic

On the Role of Variable Infectivity in the Dynamics of the Human Immunodeficiency Virus Epidemic

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect

Media alert in an SIS epidemic model with logistic growth

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