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A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion.

ABSTRACT: In this paper, we present a regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion. We utilize the Markov semigroup theory to obtain the existence of a unique stable stationary distribution. We prove that the densities of the distributions of the solutions can converge in L¹ to an invariant density under certain condition. Moreover, the sufficient conditions for the extinction of the disease, which means the disease will die out with probability one, are given in two cases. Meanwhile, we obtain a threshold parameter which can be utilized in identifying the stochastic extinction and persistence of the disease. Some numerical simulations are given to illustrate the analytical results.

SUBMITTER: Cao Z

PROVIDER: S-EPMC6650464 | biostudies-literature | 2019 Jul

REPOSITORIES: biostudies-literature

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A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion.

Cao Zhongwei Z Liu Xu X Wen Xiangdan X Liu Liya L Zu Li L

Scientific reports 20190723 1

In this paper, we present a regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion. We utilize the Markov semigroup theory to obtain the existence of a unique stable stationary distribution. We prove that the densities of the distributions of the solutions can converge in L<sup>1</sup> to an invariant density under certain condition. Moreover, the sufficient conditions for the extinction of the disease, which means the disease will die out with probabi ...[more]

PMID: 31337826

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Project description:Dengue, a mosquito-borne infectious disease caused by the dengue viruses, is present in many parts of the tropical and subtropical regions of the world. All four serotypes of dengue viruses are endemic in Singapore, an equatorial city-state. Frequent outbreaks occur, sometimes leading to national epidemics. However, few studies have attempted to characterize breakpoints which precede large rises in dengue case counts. In this paper, Bayesian regime switching (BRS) models were employed to infer epidemic and endemic regimes of dengue transmissions, each containing regime specific autoregressive processes which drive the growth and decline of dengue cases, estimated using a custom built multi-move Gibbs sampling algorithm. Posterior predictive checks indicate that BRS replicates temporal trends in Dengue transmissions well and nowcast accuracy assessed using a post-hoc classification scheme showed that BRS classification accuracy is robust even under limited data with the AUC-ROC at 0.935. LASSO-based regression and bootstrapping was used to account for plausibly high dimensions of climatic factors affecting Dengue transmissions, which was then estimated using cross-validation to conduct statistical inference on long-run climatic effects on the estimated regimes. BRS estimates epidemic and endemic regimes of dengue in Singapore which are characterized by persistence across time, lasting an average of 20 weeks and 66 weeks respectively, with a low probability of transitioning away from their regimes. Climate analysis with LASSO indicates that long-run climatic effects up to 20 weeks ago do not differentiate epidemic and endemic regimes. Lastly, by fitting BRS to simulated disease data generated from a stochastic Susceptible-Infected-Recovered model, mechanistic links between infectivity and regimes classified using BRS were provided. The model proposed could be applied to other localities and diseases under minimal data requirements where transmission counts over time are collected.

Dataset Information

A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion.

Publications

A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion.

Similar Datasets

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