In this work, we investigate a stochastic epidemic model with relapse and distributed delay. First, we prove that our model possesses and unique global positive solution. Next, by means of the Lyapunov method, we determine some sufficient criteria for the extinction of the disease and its persistence. In addition, we establish the existence of a unique stationary distribution to our model. Finally, we provide some numerical simulations for the stochastic model to assist and show the applicability and efficiency of our results.

Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel

In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and telegraph noise incorporating general incidence rate. Firstly, we investigate the existence and uniqueness of a global positive solution. Then, we establish the stochastic threshold for the extinction and the persistence of the disease. The data from Indian states, are used to confirm the results established along this paper.

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

From 7 November 2020, Greece adopted a second nationwide lockdown policy to mitigate the transmission of SARS-CoV-2 (the first took place from 23 March to 4 May 2020), just as the second wave of COVID-19 was advancing, as did other European countries. To secure the full benefits of mass vaccination, which started in early January 2021, it is of utmost importance to complement it with mid-term non-pharmaceutical interventions (NPIs). The objective was 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 15 February 2021 and a post-vaccination SVEIR from 15 February 2021 to 30 June 2021) is developed. Three scenarios are assessed for the first phase: (a) A baseline scenario, which lifts the national lockdown and all NPIs in January 2021; (b) a "semi-lockdown" scenario with school opening, partial retail sector operation, universal mask wearing, and social distancing/teleworking in January 2021; and (c) a "rolling lockdown" scenario combining a partial lifting of measures in January 2021 followed by a third nationwide lockdown in February 2021. In the second phase three scenarios with different vaccination rates are assessed. Publicly available data along with some 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 clearly outperforms the third lockdown scenario (5.7% less expected fatalities); the second phase is extremely sensitive on the availability of sufficient vaccine supplies and high vaccination rates.

https://www.mdpi.com/1660-4601/18/5/2497/pdf

A Two-Phase Stochastic Dynamic Model for COVID-19 Mid-Term Policy Recommendations in Greece: A Pathway towards Mass Vaccination.

This manuscript presents a nonlinear fractional order Hepatitis B virus (HBV) model with saturated incidence. Model governing equations are defined using Caputo fractional derivatives. We use the Adams–Bashforth-Moulton technique to compute numerical solutions of the presented epidemic model. Generally, fractional derivatives are used to model real-world phenomena that contains nonlocal effects, history and/or memory. The main objective is to develop and explore the dynamics of an HBV fractional derivative epidemic model via the Caputo definition. Firstly, we discuss the model basic properties which include positivity of solutions and the invariant regions where the solution set is bounded using the generalized fractional mean value theorem. The model dynamics are described based on the reproduction number R 0 . Thereafter, we use the fractional Routh-Hurwitz stability criterion as well as simple matrix algebra to determine sufficient conditions for the stability of the equilibrium points. Lastly, we present graphical representation of numerical results. The results indicate the importance of fractional order in modeling HBV transmission dynamics and ensures that by including the memory effects, the model is more appropriate and insightful for such a study.

A fractional order differential equation model for Hepatitis B virus with saturated incidence

In this paper, the qualitative analysis of a stochastic two delayed epidemic model incorporating Levy processes with a general non-linear incidence transmission is considered. Our analysis show tha...

Stochastic analysis of a two delayed epidemic model incorporating Lévy processes with a general non-linear transmission

In this paper, we investigate a stochastic hepatitis B epidemic model driven by Levy noise. We prove the existence of a unique global positive solution and we present sufficient conditions to derive extinction and persistence in mean of the disease.

A stochastic Hepatitis B epidemic model driven by Lévy noise

In this paper, we discuss an epidemic model with double hypothesis combined two different transmission mechanisms. First, we prove the local asymptotic stability of the equilibrium solutions of deterministic system. Moreover we establish the global stability for the free equilibrium. Second, we show for stochastic system the extinction and persistence in mean of the disease, under some conditions on parameters of the model. Finally, numerical simulations are used to confirm our analytical results.

Brahim Boukanjime

Papers

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

A stochastic Hepatitis B epidemic model driven by Lévy noise

Stochastic analysis of a two delayed epidemic model incorporating Lévy processes with a general non-linear transmission

Analysis of a deterministic and a stochastic epidemic model with two distinct epidemics hypothesis

A Markovian regime-switching stochastic hybrid time-delayed epidemic model with vaccination