A core group model for disease transmission

Hadeler, K. P.; Castillo‐Chavez, Carlos

doi:10.1016/0025-5564(94)00066-9

Cited by 212 publications

(147 citation statements)

References 13 publications

(20 reference statements)

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“…It is important to distinguish our findings from those of previous models of 'behaviour change' in STD epidemics (Hadeler & Castillo-Chavez 1995;Hyman & Li 1997;Hsieh & Sheu 2001). In these studies, susceptible individuals may choose to change their rate of acquiring new sexual partners (c FD ) or the probability of transmission per partnership ( p FD ), typically as a result of public-education campaigns or community awareness of disease risk.…”

Section: Discussionmentioning

confidence: 96%

Frequency–dependent incidence in models of sexually transmitted diseases: portrayal of pair–based transmission and effects of illness on contact behaviour

Lloyd‐Smith

Getz

Westerhoff³

2004

Proc. R. Soc. Lond. B

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We explore the transmission process for sexually transmitted diseases (STDs). We derive the classical frequency-dependent incidence mechanistically from a pair-formation model, using an approximation that applies to populations with rapid pairing dynamics (such as core groups or non-pair-bonding animals). This mechanistic derivation provides a framework to assess how accurately frequency-dependent incidence portrays the pair-based transmission known to underlie STD dynamics. This accuracy depends strongly on the disease being studied: frequency-dependent formulations are more suitable for chronic less-transmissible infections than for transient highly transmissible infections. Our results thus support earlier proposals to divide STDs into these two functional classes, and we suggest guidelines to help assess under what conditions each class can be appropriately modelled using frequency-dependent incidence. We then extend the derivation to include situations where infected individuals exhibit altered pairing behaviour. For four cases of increasing behavioural complexity, analytic expressions are presented for the generalized frequency-dependent incidence rate, basic reproductive number (R 0 ) and steady-state prevalence (i ϱ ) of an epidemic. The expression for R 0 is identical for all cases, giving refined insights into determinants of invasibility of STDs. Potentially significant effects of infection-induced changes in contact behaviour are illustrated by simulating epidemics of bacterial and viral STDs. We discuss the application of our results to STDs (in humans and animals) and other infectious diseases.

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Section: Discussionmentioning

confidence: 96%

Frequency–dependent incidence in models of sexually transmitted diseases: portrayal of pair–based transmission and effects of illness on contact behaviour

Lloyd‐Smith

Getz

Westerhoff³

2004

Proc. R. Soc. Lond. B

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“…It seems to us that the occurrence of backward (subcritical) bifurcations, the existence of multiple infected stationary states, and hysteresis phenomena (including abrupt changes in disease prevalence levels) are but a few of the components that are supportive of disease reemergence. Models that generate this type of landscapes must be understood since they provide useful insights in the study of disease re-emrgence and evolution (see Castillo-Chavez et al 1989, Huang et al 1992, Hadeler et al 1995and Feng et al 2000.…”

Section: Resultsmentioning

confidence: 99%

“…One of the possible consequences associated with such memory loss is the remergence of HIV (as predicted by Hadeler and Castilla-Chavez, 1995). This paper is organized as follows: Section 1 introduces an age-structure model with prevalence dependent recruitment rates; Section 2 looks at the local stability of the infection-free distribution; Section 3 states the conditions for the existence of nonuniform endemic age distributions and gives an example where endemic age distributions are possible even though R0 < 1.…”

Section: Introductionmentioning

confidence: 99%

Age-Structured Core Group Model and its Impact on STD Dynamics

Castillo‐Chavez

Huang

2002

Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory

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The recruitment of new susceptibles into a core group of sexually-active individuals may depend on the current levels of infection within a population. We extend the formalism ofHadeler and Castille-Chavez (1995), that includes prevalence dependent recruitment rates, to include age structure within core and noncore populations. Some mathematical results are stated but only a couple of proofs are included since our objectives are to highlight the modeling process and the dynamic possibilities. This paper concludes with an example where endemic distributions can be supported when the basic reproductive number Ro is less than one. Systems that re capable of supporting multiple attractors are more likely to support disease re-emergence. This model is likely to support stable multiple attractors when Ro < 1. Abstract The recruitment of new suceptibles into a core group of sexually-active individuals may depend on the current levels of infection within a population. We extend Age-structured

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“…[6,17,21,29,40,42,46,52,53,59]. It is interesting to contrast the bifurcation behaviour of theAE model presented here with a BB, see Figure 6a and 6b, respectively.…”

Section: Differences To Backward Bifurcationsmentioning

confidence: 88%

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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A core group model for disease transmission

Abstract: Models for sexually

Cited by 212 publications

References 13 publications

Frequency–dependent incidence in models of sexually transmitted diseases: portrayal of pair–based transmission and effects of illness on contact behaviour

Frequency–dependent incidence in models of sexually transmitted diseases: portrayal of pair–based transmission and effects of illness on contact behaviour

Age-Structured Core Group Model and its Impact on STD Dynamics

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

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