TITLE:
A Comparison of Deterministic and Stochastic Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) Models
AUTHORS:
Abdelmalik Moujahid, Fernando Vadillo
KEYWORDS:
Persistence Time, Epidemic Dynamics, Stochastic Epidemic Models, Finite Element Method
JOURNAL NAME:
Open Journal of Modelling and Simulation,
Vol.9 No.3,
July
19,
2021
ABSTRACT: In this paper we build and analyze two stochastic epidemic models with
death. The model assumes that only susceptible individuals (S) can get infected (I) and may die
from this disease or a recovered individual becomes susceptible again (SIS
model) or completely immune (SIR Model) for the remainder of the study period.
Moreover, it is assumed there are no births, deaths, immigration or emigration
during the study period; the community is said to be closed. In these infection
disease models, there are two central questions: first it is the disease
extinction or not and the second studies the time elapsed for such extinction,
this paper will deal with this second question because the first answer
corresponds to the basic reproduction number defined in the bibliography. More
concretely, we study the mean-extinction of the diseases and the technique used
here first builds the backward Kolmogorov differential equation and then solves
it numerically using finite element method with FreeFem++. Our contribution and
novelty are the following: however the reproduction number effectively concludes the
extinction or not of the disease, it does not help to know its extinction times
because example with the same reproduction numbers has very different time.
Moreover, the SIS model is slower, a result that is not surprising, but this
difference seems to increase in the stochastic models with respect to the
deterministic ones, it is reasonable to assume some uncertainly.