Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps

2017 ◽  
Vol 471 ◽  
pp. 767-777 ◽  
Author(s):  
Xinhong Zhang ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Bashir Ahmad
Keyword(s):  
Sis Model ◽  
Lévy Jumps ◽  
Epidemic Diseases ◽  
Stochastic Sis Model

scholarly journals A Stochastic Kinetic Type Reactions Model for COVID-19

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1221
Author(s):  
Giorgio Sonnino ◽  
Fernando Mora ◽  
Pasquale Nardone
Keyword(s):  
Real Data ◽  
Stochastic Noise ◽  
Mathematical Basis ◽  
Sis Model ◽  
Theoretical Predictions ◽  
Coronavirus Infection ◽  
Massive Distribution ◽  
Second Wave ◽  
Stochastic Sis Model

We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density functions, were duly computed. Our models take into account the adoption of lockdown measures as well as the crucial role of hospitals and health care institutes. To accomplish this work we adopt a kinetic-type reaction approach where the modelling of the lockdown measures is obtained by introducing a new mathematical basis and the intensity of the stochastic noise is derived by statistical mechanics. We analysed two scenarios: the stochastic SIS-model (Susceptible ⇒ Infectious ⇒ Susceptible) and the stochastic SIS-model integrated with the action of the hospitals; both models take into account the lockdown measures. We show that, for the case of the stochastic SIS-model, once the lockdown measures are removed, the Coronavirus infection will start growing again. However, the combined contributions of lockdown measures with the action of hospitals and health institutes is able to contain and even to dampen the spread of the SARS-CoV-2 epidemic. This result may be used during a period of time when the massive distribution of vaccines in a given population is not yet feasible. We analysed data for USA and France. In the case of USA, we analysed the following situations: USA is subjected to the first wave of infection by Coronavirus and USA is in the second wave of SARS-CoV-2 infection. The agreement between theoretical predictions and real data confirms the validity of our approach.

The quasi-stationary distribution of the closed endemic sis model

1996 ◽  
Vol 28 (3) ◽  
pp. 895-932 ◽  
Author(s):  
Ingemar Nåsell
Keyword(s):  
Stationary Distribution ◽  
Geometric Distribution ◽  
Threshold Value ◽  
Basic Reproduction Ratio ◽  
Sis Model ◽  
Reproduction Ratio ◽  
Time To Extinction ◽  
Extreme Distributions ◽  
Stochastic Sis Model ◽  
Quasi Stationary Distribution

The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R0 passes the deterministic threshold value 1. Approximations are derived that describe these changes. The quasi-stationary distribution is approximated by a geometric distribution (discrete!) for R0 distinctly below 1 and by a normal distribution (continuous!) for R0 distinctly above 1. Uniformity of the approximation with respect to R0 allows one to study the transition between these two extreme distributions. We also study the time to extinction and the invasion and persistence thresholds of the model.

Threshold behavior of a stochastic SIS model with Le´vy jumps

2016 ◽  
Vol 275 ◽  
pp. 255-267 ◽  
Author(s):  
Yanli Zhou ◽  
Sanling Yuan ◽  
Dianli Zhao
Keyword(s):  
Threshold Behavior ◽  
Sis Model ◽  
Stochastic Sis Model

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

2019 ◽  
Vol 523 ◽  
pp. 677-690 ◽  
Author(s):  
Tomás Caraballo ◽  
Adel Settati ◽  
Mohamed El Fatini ◽  
Aadil Lahrouz ◽  
Abdelouahid Imlahi
Keyword(s):  
Global Stability ◽  
Lévy Noise ◽  
Sis Model ◽  
Positive Recurrence ◽  
Noise Perturbation ◽  
Levy Noise ◽  
Stochastic Sis Model

The quasi-stationary distribution of the closed endemic sis model

1996 ◽  
Vol 28 (03) ◽  
pp. 895-932 ◽  
Author(s):  
Ingemar Nåsell
Keyword(s):  
Stationary Distribution ◽  
Geometric Distribution ◽  
Threshold Value ◽  
Basic Reproduction Ratio ◽  
Sis Model ◽  
Reproduction Ratio ◽  
Time To Extinction ◽  
Extreme Distributions ◽  
Stochastic Sis Model ◽  
Quasi Stationary Distribution

The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R 0 passes the deterministic threshold value 1. Approximations are derived that describe these changes. The quasi-stationary distribution is approximated by a geometric distribution (discrete!) for R 0 distinctly below 1 and by a normal distribution (continuous!) for R 0 distinctly above 1. Uniformity of the approximation with respect to R 0 allows one to study the transition between these two extreme distributions. We also study the time to extinction and the invasion and persistence thresholds of the model.

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