Dynamic phenomena arising from an extended Core Group model

Greenhalgh, David; Griffiths, Martin

doi:10.1016/j.mbs.2009.08.003

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…Adaptive behavior of individuals to disease (Hadeler & Castillo-Chavez 1995; Huang et al 2002; Greenhalgh & Griffiths 2009; Fenichel et al 2011). …”

Section: Multiple Interior Equilibria and Possible Bifurcationsmentioning

confidence: 99%

A simple epidemiological model for populations in the wild with Allee effects and disease-modified fitness

Kang

Castillo‐Chavez²

2014

Discrete &Amp; Continuous Dynamical Systems - B

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The study of the dynamics of human infectious disease using deterministic models is typically carried out under the assumption that a critical mass of individuals is available and involved in the transmission process. However, in the study of animal disease dynamics where demographic considerations often play a significant role, this assumption must be weakened. Models of the dynamics of animal populations often naturally assume that the presence of a minimal number of individuals is essential to avoid extinction. In the ecological literature, this a priori requirement is commonly incorporated as an Allee effect. The focus here is on the study disease dynamics under the assumption that a critical mass of susceptible individuals is required to guarantee the population's survival. Specifically, the emphasis is on the study of the role of an Allee effect on a Susceptible-Infectious (SI) model where the possibility that susceptible and infected individuals reproduce, with the S-class the best fit. It is further assumed that infected individuals loose some of their ability to compete for resources, the cost imposed by the disease. These features are set in motion in as simple model as possible. They turn out to lead to a rich set of dynamical outcomes. This toy model supports the possibility of multi-stability (hysteresis), saddle node and Hopf bifurcations, and catastrophic events (disease-induced extinction). The analyses provide a full picture of the system under disease-free dynamics including disease-induced extinction and proceed to identify required conditions for disease persistence. We conclude that increases in (i) the maximum birth rate of a species, or (ii) in the relative reproductive ability of infected individuals, or (iii) in the competitive ability of a infected individuals at low density levels, or in (iv) the per-capita death rate (including disease-induced) of infected individuals, can stabilize the system (resulting in disease persistence). We further conclude that increases in (a) the Allee effect threshold, or (b) in disease transmission rates, or in (c) the competitive ability of infected individuals at high density levels, can destabilize the system, possibly leading to the eventual collapse of the population. The results obtained from the analyses of this toy model highlight the significant role that factors like an Allee effect may play on the survival and persistence of animal populations. Scientists involved in biological conservation and pest management or interested in finding sustainability solutions, may find these results of this study compelling enough to suggest additional focused research on the role of disease in the regulation and persistence of animal populations. The risk faced by endangered species may turn out to be a lot higher than initially thought.

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“…Adaptive behavior of individuals to disease (Hadeler & Castillo-Chavez 1995; Huang et al 2002; Greenhalgh & Griffiths 2009; Fenichel et al 2011). …”

Section: Multiple Interior Equilibria and Possible Bifurcationsmentioning

confidence: 99%

A simple epidemiological model for populations in the wild with Allee effects and disease-modified fitness

Kang

Castillo‐Chavez²

2014

Discrete &Amp; Continuous Dynamical Systems - B

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“…When the population growth rate is positive at low population 15 size or density, the Allee effect is said to be weak. For the weak Allee effect 16 no threshold of the population size or density exists. 17 In recent years, a number of authors reported that models with an Allee 18 effect in the host demographics exhibit complex dynamics such as periodic 19 oscillation, multiple stable steady states, and a series of bifurcations.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of an epidemiological model with a demographic Allee effect

Usaini

Lloyd

Anguelov

et al. 2017

Mathematics and Computers in Simulation

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Vaccination based control of infections in SIRS models with reinfection: special reference to pertussis

2012

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The aim of this paper is to study the impact of introducing a partially protective vaccine on the dynamics of infection in SIRS models where primary and secondary infections are distinguished. We investigate whether a public health strategy based solely on vaccinating a proportion of newborns can lead to an effective control of the disease. In addition to carrying out the qualitative analysis, the findings are further explained by numerical simulations. The model exhibits backward bifurcation for certain values of the parameters. In these cases the standard basic reproduction number (obtained by inspection of the uninfected state) is not significant. The key threshold is the reinfection level which depends on the relative transmissibility (susceptibility) of secondary, with respect to primary, infected (susceptible) individuals and the relative loss of immunity of vaccinated, with respect to recovered, individuals. If one or all of these ratios decrease, then the threshold increases which increases the possibility to contain the infection by vaccination. The analysis shows further that symptomatic infections can be eliminated by vaccination solely.

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Dynamic phenomena arising from an extended Core Group model

Cited by 5 publications

References 19 publications

A simple epidemiological model for populations in the wild with Allee effects and disease-modified fitness

A simple epidemiological model for populations in the wild with Allee effects and disease-modified fitness

Dynamical behavior of an epidemiological model with a demographic Allee effect

Vaccination based control of infections in SIRS models with reinfection: special reference to pertussis

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