Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel. (April 2020)

• Record Type: Journal Article
• Authors: Caraballo, Tomás; Fatini, Mohamed El; Khalifi, Mohamed El; Gerlach, Richard; Pettersson, Roger
• Is Part Of: Chaos, solitons and fractals. Volume 133(2020)
• Publication Date: 2020-04
• Subjects: Epidemic model -- Distributed delay -- Extinction -- Persistence -- Stationary distribution; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.109643
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: 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.