Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching

Boukanjime, Brahim; Caraballo, Tomás; Fatini, Mohamed El; Khalifi, Mohamed El

doi:10.1016/j.chaos.2020.110361

Cited by 47 publications

(31 citation statements)

References 23 publications

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“…Therefore, the saturation value x ∞ (p) = lim t→∞ x(t) should exceed the value given by Eq. (15). Figure 6 shows dependence of asymptotic value of solution to Eq.…”

Section: >mentioning

confidence: 99%

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Epidemic transmission with quarantine measures: application to COVID-19

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Czerniawski

Ignatov

2021

Preprint

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Equations for infection spread in a closed population are found in discrete approximation, corresponding to the published statistical data, and in continuous time in the form of delay differential equations. We consider the epidemic as dependent upon four key parameters: the size of population involved, the mean number of dangerous contacts of one infected person per day, the probability to transmit infection due to such contact and the mean duration of disease. In the simplest case of free-running epidemic in an infinite population, the number of infected rises exponentially day by day. Here we show the model for epidemic process in a closed population, constrained by isolation, treatment and so on. The four parameters introduced here have the clear sense and are in association with the well-known concept of reproduction number in the continuous susceptible--infectious--removed, susceptible--exposed--infectious--removed (SIR, SEIR) models. We derive the initial rate of infection spread from the published statistical data for the initial stage of epidemic, when the quarantine measures were absent. On this basis, we can found the corresponding basic reproduction number mentioned above. Our approach allows evaluating the influence of quarantine measures on free pandemic process that leads to the time-dependent rate of infection and suppression of infection. We found a good correspondence of the theory and reliable statistical data. The initially formulated discrete model, describing epidemic course day by day is transferred to differential form. The conditions for saturation of epidemic are found by solving the delay differential equations. They differ essentially from ones in SIR model due to finite delay, typical for COVID-19. The proposed model opens up the possibility to predict the optimal level of social quarantine measures. The model is quite flexible and it can be extended to more complex cases.

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“…Therefore, the saturation value x ∞ (p) = lim t→∞ x(t) should exceed the value given by Eq. (15). Figure 6 shows dependence of asymptotic value of solution to Eq.…”

Section: >mentioning

confidence: 99%

“…There are stochastic (e.g., [15,16]) and deterministic approaches to the description of epidemic course. The latter include the SIR, SEIR models and their modifications.…”

Section: Introductionmentioning

confidence: 99%

Epidemic transmission with quarantine measures: application to COVID-19

Trigger

Czerniawski

Ignatov

2021

Preprint

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“…By December 31st, 2020, there were 138,850 diagnosed cases and 4,838 deaths. As of December 31 st , 2021, the corresponding naive case fatality rate in Greece is 3.48% and the mortality rate is approximately 45 deaths per 100,000 population, ranking the country 126 th out of 171 worldwide and 17 th out of 50 Europe-wide 7 .…”

Section: Model Equationsmentioning

confidence: 99%

A two-phase stochastic dynamic model for COVID-19 mid-term policy recommendations in Greece: a pathway towards mass vaccination

Rachaniotis

Dasaklis

Fotopoulos

et al. 2021

Preprint

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From November 7th, 2020, Greece adopted a second nationwide lockdown policy to mitigate the transmission of SARS-CoV-2 (the first took place from March 23rd till May 4th, 2020), just as the second wave of COVID-19 was advancing, as did other European countries. In the light of the very promising voluntary mass vaccination, which will start in January 2021, it is of utmost importance for the country to plan to complement vaccination with mid-term Non-Pharmaceutical Interventions (NPIs). The objective is to minimize human losses and to limit social and economic costs. In this paper a two-phase stochastic dynamic network compartmental model (a pre-vaccination SEIR until February 15th, 2021 and a post-vaccination SVEIR from February 15th, 2021 to June 30th, 2021) is developed. Three scenarios are assessed in the first phase: (a) a baseline scenario, which lifts the national lockdown and all NPIs on January 2021, (b) a “semi-lockdown” scenario with school opening, partial retail sector operation, universal mask wearing and social distancing/teleworking on January 2021 and (c) a “rolling lockdown” scenario combining a partial lifting of measures in January 2021 followed by a third imposed nationwide lockdown in February 2021. In the second phase three scenarios with different vaccination rates are assessed. Publicly available data along with some preliminary first results of the SHARE COVID-19 survey conducted in Greece are used as input. The results regarding the first phase indicate that the “semi-lockdown” scenario outperforms the third lockdown scenario (5.7% less expected fatalities), whereas in the second phase it is of great importance to ensure a sufficient vaccine supply and high vaccination rates.

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“…Applying Lyapunov method Zhang and Wang [ 45 ] achieved the conditions for the stochastic stability, persistence and extinction of an SEIR model driven simultaneously by white and Lévy noises (termed jumps) which can capture the wide spread of infectious diseases caused by medical negligence. More recently, Boukanjime et al [ 46 ] utilized a stochastic SEIR model to describe the COVID-19 transmission dynamics affected by mixture of white and telegraph noises and investigated the extinction and persistence in the mean of the COVID-19 epidemic in Indian states in terms of the stochastic threshold .…”

Section: Introductionmentioning

confidence: 99%

“…Artalejo and his coauthors [ 50 ] formulated a stochastic SEIR model described by a continuous-time Markov chain and developed efficient computational procedures for the distribution of the duration of an outbreak. Another frequently used approach is to incorporate the noises (such as the white, color, Lévy, telegraph noises or the coupling noises between them) into certain deterministic epidemic models [ 20 , 43 – 46 ]. This approach is mainly involved in the following several different forms of perturbations: the noises may perturb model parameters [ 23 , 52 – 56 ], or be proportional to the distance between the state variables and the endemic equilibria of the deterministic models [ 24 , 57 , 58 ], or proportional to the state variables measuring population densities [ 19 , 25 , 43 , 47 , 59 ], with the advantage of good understanding the stochastic dynamics in long time of these models from the theoretical analysis perspective.…”

Section: Introductionmentioning

confidence: 99%

A stochastic epidemic model with infectivity in incubation period and homestead–isolation on the susceptible

Shangguan

Liu

Wang

et al. 2021

J. Appl. Math. Comput.

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A stochastic epidemic model with infectivity rate in incubation period and homestead–isolation on the susceptible is developed with the aim of revealing the effect of stochastic white noise on the long time behavior. A good understanding of extinction and strong persistence in the mean of the disease is obtained. Also, we derive sufficient criteria for the existence of a unique ergodic stationary distribution of the model. Our theoretical results show that the suitably large noise can make the disease extinct while the relatively small noise is advantageous for persistence of the disease and stationary distribution.

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Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching

Cited by 47 publications

References 23 publications

Epidemic transmission with quarantine measures: application to COVID-19

Epidemic transmission with quarantine measures: application to COVID-19

A two-phase stochastic dynamic model for COVID-19 mid-term policy recommendations in Greece: a pathway towards mass vaccination

A stochastic epidemic model with infectivity in incubation period and homestead–isolation on the susceptible

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