Approximating time to extinction for endemic infection models

Clancy, Damian; Tjia, Elliott

doi:10.48550/arxiv.1707.02758

Cited by 1 publication

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“…This approach seems reasonable in terms of qualitative comparisons between infection models, and is common in the literature. However, the approach is known to give a very bad numerical approximation to mean persistence time, with incorrect leading-order asymptotic behaviour, due to the failure in the lower tail of the normal approximation to the quasi-stationary distribution [11,9]. The methods of the current paper, in contrast, deal directly with the expected persistence time and yield correct leading-order asymptotic formulae.…”

Section: Generalising the Infectious Period Distributionmentioning

confidence: 93%

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Persistence time of SIS infections in heterogeneous populations and networks

Clancy

2018

J. Math. Biol.

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For a susceptible–infectious–susceptible infection model in a heterogeneous population, we present simple formulae giving the leading-order asymptotic (large population) behaviour of the mean persistence time, from an endemic state to extinction of infection. Our model may be interpreted as describing an infection spreading through either (1) a population with heterogeneity in individuals’ susceptibility and/or infectiousness; or (2) a heterogeneous directed network. Using our asymptotic formulae, we show that such heterogeneity can only reduce (to leading order) the mean persistence time compared to a corresponding homogeneous population, and that the greater the degree of heterogeneity, the more quickly infection will die out.

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Section: Generalising the Infectious Period Distributionmentioning

confidence: 93%

“…For the SIS model with Erlang-distributed infectious periods in a homogeneous population (k = 1), the solution U (θ) to the relevant Hamilton-Jacobi equation was found in [9] to be…”

Section: Generalising the Infectious Period Distributionmentioning

confidence: 99%

Persistence time of SIS infections in heterogeneous populations and networks

Clancy

2018

J. Math. Biol.

Self Cite

View full text Add to dashboard Cite

show abstract

Approximating time to extinction for endemic infection models

Cited by 1 publication

References 0 publications

Persistence time of SIS infections in heterogeneous populations and networks

Persistence time of SIS infections in heterogeneous populations and networks

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