scholarly journals Persistence-time estimation for some stochastic SIS epidemic models

2015 ◽  
Vol 20 (9) ◽  
pp. 2933-2947 ◽  
Author(s):  
Francisco de la Hoz ◽  
Anna Doubova ◽  
Fernando Vadillo
Keyword(s):  
Time Estimation ◽  
Epidemic Models ◽  
Persistence Time ◽  
Sis Epidemic

The explicit series solution of SIR and SIS epidemic models

2009 ◽  
Vol 215 (2) ◽  
pp. 653-669 ◽  
Author(s):  
Hina Khan ◽  
Ram N. Mohapatra ◽  
K. Vajravelu ◽  
S.J. Liao
Keyword(s):  
Series Solution ◽  
Epidemic Models ◽  
Sis Epidemic

scholarly journals Discrete and continuous SIS epidemic models: A unifying approach

2014 ◽  
Vol 18 ◽  
pp. 83-95 ◽  
Author(s):  
Fabio A.C.C. Chalub ◽  
Max O. Souza
Keyword(s):  
Epidemic Models ◽  
Sis Epidemic

scholarly journals On Deterministic and Stochastic Multiple Pathogen Epidemic Models

Epidemiologia ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 325-337
Author(s):  
Fernando Vadillo
Keyword(s):  
Variable Coefficients ◽  
Epidemic Models ◽  
Kolmogorov Equation ◽  
The Finite Element Method ◽  
Persistence Time ◽  
Main Challenge ◽  
Stochastic Epidemic ◽  
The Mean ◽  
Backward Kolmogorov Equation ◽  
Multiple Pathogen

In this paper, we consider a stochastic epidemic model with two pathogens. In order to analyze the coexistence of two pathogens, we compute numerically the expectation time until extinction (the mean persistence time), which satisfies a stationary partial differential equation with degenerate variable coefficients, related to backward Kolmogorov equation. I use the finite element method in order to solve this equation, and we implement it in FreeFem++. The main conclusion of this paper is that the deterministic and stochastic epidemic models differ considerably in predicting coexistence of the two diseases and in the extinction outcome of one of them. Now, the main challenge would be to find an explanation for this result.

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