Stochastic Modeling of Infectious Disease

Select Volume / Issue:

• Volume 8,Issue 6,Nov. 2020

Year:

2020

Type of Publication:

Article

Keywords:

Vital Dynamics, Infectious Disease, Stochastic Model, Seasonal Forcing, SIR Model

Authors:

M. D. Alsulami

Journal:

IJISM

Volume:

8

Number:

6

Pages:

262-269

Month:

November

ISSN:

2347-9051

Abstract:

Here we present three versions of an SIR model including death, birth, infection, and recovery terms. We began with an unforced model, which we nondimensionalized and analyzed. It was found to have two steady states: one where the entire population has become susceptible and another with less easily interpretable population levels. The states were mutually exclusive, depending on the infection and recovery terms, and featured slightly different behaviors. We then altered the model in an attempt to resemble data from the CDC. First, a seasonal forcing term was added that had a period of half of a year. With this term, the model produced a profile that resembled a CDC yearly profile in that the infected population of both varied on the order of a year. Next, a stochastic or random model was created that treated each term of our non-dimensionalized equation as random events. A random event was triggered by each time step, creating profiles that appeared to replicate the randomness of CDC data.

Full text: IJISM_921_FINAL.pdf [Bibtex]