Epidemics on networks with heterogeneous population and stochastic infection rates

Bonaccorsi, Stefano; Ottaviano, Stefania

doi:10.1016/j.mbs.2016.07.002

Cited by 12 publications

(8 citation statements)

References 41 publications

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“…Specifically, we have studied the dynamic behaviour of the hybrid system (4), that is composed of m subsystems switching from one state to another according to the law of a Markov chain. In this way, we have extended our study in [3].…”

Section: Discussionmentioning

confidence: 79%

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A stochastic differential equation SIS model on network under Markovian switching

Ottaviano¹,

Bonaccorsi²

2020

Preprint

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We study a stochastic SIS epidemic dynamics on network, under the effect of a Markovian regime-switching. We first prove the existence of a unique global positive solution, and find a positive invariant set for the system. Then, we find sufficient conditions for a.s. extinction and stochastic permanence, showing also their relation with the stationary probability distribution of the Markov chain that rules the switching. We provide an asymptotic lower bound for the time average of the solution sample path, under the conditions ensuring stochastic permanence. From this bound we are able to prove the existence of an invariant probability measure.

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Section: Discussionmentioning

confidence: 79%

“…We add another kind of random fluctuations on the model, by considering white noise (see e.g., [3,19,29,15]). White noise is a useful mathematical idealization for representing stochastic disturbances fluctuating rapidly, which are assumed to be uncorrelated for different instant of time [1].…”

Section: Introductionmentioning

confidence: 99%

A stochastic differential equation SIS model on network under Markovian switching

Ottaviano¹,

Bonaccorsi²

2020

Preprint

Self Cite

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“…In this perspective, the SIS model was preferred to a model with immunity. Second, transitions were modeled with Poissonian probability distributions, whereas many of these processes are generally described by broader distributions [38,39] . In this context, we expect that this approximation may impact the recovery process from the state F differently than from the state I.…”

Section: Discussionmentioning

confidence: 99%

The effect of delayed awareness and fatigue on the efficacy of self-isolation in epidemic control

de Meijere,

Colizza,

Valdano

et al. 2021

Preprint

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The isolation of infectious individuals is a key measure of public health for the control of communicable diseases. However, involving a strong perturbation of daily life, it often causes psychosocial distress, and severe financial and social costs. These may act as mechanisms limiting the adoption of the measure in the first place or the adherence throughout its full duration. In addition, difficulty of recognizing mild symptoms or lack of symptoms may impact awareness of the infection and further limit adoption. Here, we study an epidemic model on a network of contacts accounting for limited adherence and delayed awareness to self-isolation, along with fatigue causing overhasty termination. The model allows us to estimate the role of each ingredient and analyze the tradeoff between adherence and duration of self-isolation. We find that the epidemic threshold is very sensitive to an effective compliance that combines the effects of imperfect adherence, delayed awareness and fatigue. If adherence improves for shorter quarantine periods, there exists an optimal duration of isolation, shorter than the infectious period. However, heterogeneities in the connectivity pattern, coupled to a reduced compliance for highly active individuals, may almost completely offset the effectiveness of self-isolation measures on the control of the epidemic.

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“…It is more suitable to describe the disease spreading with stochastic differential equations with Brownian motion as noise, i.e., stochastic epidemic model. In recent years, many scholars have focused on stochastic epidemic models on complex networks and a lot of results have emerged [10,11,12].…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the works in [9,10,11,12], we will consider the following new SIS model with stochastic perturbation…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviors of a New Sis Epidemic Model on Scale-Free Networks With Stochastic Perturbation

Sun¹,

Liu²

2021

Int. J. of Appl. Math.

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A new SIS epidemic model on scale-free networks with stochastic perturbation is considered. We deduce that dynamical behaviors of the model are related to the basic reproduction number R 0 of the corresponding deterministic model. Under the conditions that the intensities of white noises interference are sufficiently weak, the solution of the model oscillates around the disease-free equilibrium of the corresponding deterministic model when R 0 < 1, whereas, the disease will be persistent when R 0 > 1.

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Epidemics on networks with heterogeneous population and stochastic infection rates

Cited by 12 publications

References 41 publications

A stochastic differential equation SIS model on network under Markovian switching

A stochastic differential equation SIS model on network under Markovian switching

The effect of delayed awareness and fatigue on the efficacy of self-isolation in epidemic control

Dynamical Behaviors of a New Sis Epidemic Model on Scale-Free Networks With Stochastic Perturbation

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