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

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.Ministerio de Ciencia, Innovación y Universidades (MICINN). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER

A stochastic SIRI epidemic model with relapse and media coverage

This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic model with relapse and media coverage. We also study the dynamical properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we show the existence of a stationary distribution. Numerical simulations are presented to confirm the theoretical results.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía)Faculty of Sciences (Ibn Tofail University

A stochastic SIRI epidemic model with Lévy noise

Some diseases such as herpes, bovine and human tuberculosis exhibit relapse in which the recovered individuals do not acquit permanent immunity but return to infectious class. Such diseases are modeled by SIRI models. In this paper, we establish the existence of a unique global positive solution for a stochastic epidemic model with relapse and jumps. We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we present some numerical results to support the theoretical work

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

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

Dynamics of an SIR epidemic model with limited medical resources, revisited and corrected

This paper generalizes and corrects a famous paper (more than 200 citations) concerning Hopf and Bogdanov-Takens bifurcations due to L. Zhou and M. Fan, "Dynamics of an SIR epidemic model with limited medical resources revisited", in which we discovered a significant numerical error. Importantly, unlike the paper of Zhou and Fan and several other papers that followed them, we offer a notebook where the reader may recover all the results and modify them for analyzing similar models. Our calculations lead to the introduction of some interesting symbolic objects, "Groebner eliminated traces and determinants" - see (4.5), (4.6), which seem to have appeared here for the first time and which might be of independent interest. We hope our paper might serve as yet another alarm bell regarding the importance of accompanying papers involving complicated hand computations by electronic notebooks

Global stability and positive recurrence of a stochastic SIS model with Lévy noise perturbation

Focusing on epidemic model in random environments, this paper uses white noise and Lévy noise to model the dynamics of the SIS epidemic model subject to the random changes of the external environment. We show that the jump encourages the extinction of the disease in the population. We first, give a rigorous proof of the global stability of the disease-free equilibrium state. We also establish sufficient conditions for the persistence of the disease. The presented results are demonstrated by numerical simulations.Faculty of Sciences, Ibn Tofail University-Kénitra, Morocc

Analysis of a stochastic coronavirus (COVID-19) L´evy jump model with protective measures

This paper studied a stochastic epidemic model of the spread of the novel coronavirus (COVID19). Severe factors impacting the disease transmission are presented by white noise and compensated poisson noise with possibly infinite characteristic measure. Large time estimates are established based on Kunita’s inequality rather than Burkholder-Davis-Gundy inequality for countinuous diffusions. The effect of stochasticity is taken into account in the formulation of sufficient conditions for the extinction of COVID-19 and its persistence. Our results prove that environmental fluctuations can be privileged in controlling the pandemic behaviour. Based on real parameter values, numerical results are presented to illustrate obtained results concerning the extinction and the persistence in mean of the disease

Adaptive Mesh Refinement for a Finite Volume Method for Flow and Transport of Radionuclides in Heterogeneous Porous Media

International audienceIn this paper, we consider adaptive numerical simulation of miscible displacement problems in porous media, which are modeled by single phase flow equations. A vertex-centred finite volume method is employed to discretize the coupled system: the Darcy flow equation and the diffusion-convection concentration equation. The convection term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion-dispersion term is discretized by piecewise linear conforming finite elements. We introduce two kinds of indicators, both of them of residual type. The first one is related to time discretization and is local with respect to the time discretization: thus, at each time, it provides an appropriate information for the choice of the next time step. The second is related to space discretization and is local with respect to both the time and space variable and the idea is that at each time it is an efficient tool for mesh adaptivity. An error estimation procedure evaluates where additional refinement is needed and grid generation procedures dynamically create or remove fine-grid patches as resolution requirements change. The method was implemented in the software MELODIE, developed by the French Institute for Radiological Protection and Nuclear Safety (IRSN, Institut de Radioprotection et de Sûreté Nucléaire). The algorithm is then used to simulate the evolution of radionuclide migration from the waste packages through a heterogeneous disposal, demonstrating its capability to capture complex behavior of the resulting flow