SIS Epidemic Model Birth-and-Death Markov Chain Approach
- A.H. Nzokem
Abstract
We are interested in describing the dynamics of the infected size of the SIS Epidemic model using the Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) model is defined within a population of constant size M; the size is kept constant by replacing each death with a newborn healthy individual. The life span of each individual in the population is modelled by an exponential distribution with parameter α; the disease spreads within the population is modelled by a Poisson process with a rate λ_I. λ_I=βI(1-I/M) is similar to the instantaneous rate in the logistic population growth model. The analysis is focused on the disease outbreak, where the reproduction number (R=β/α) is greater than one. As methodology, we use both numerical and analytical approaches. The numerical approach shows that the infected size dynamics converge to a stationary stochastic process. And the analytical results determine the distribution of the stationary stochastic process as a normal distribution with mean (1-1/R)M and Variance M/R when M becomes larger.- Full Text: PDF
- DOI:10.5539/ijsp.v10n4p10
This work is licensed under a Creative Commons Attribution 4.0 License.
Journal Metrics
- h-index (December 2021): 20
- i10-index (December 2021): 51
- h5-index (December 2021): N/A
- h5-median(December 2021): N/A
( The data was calculated based on Google Scholar Citations. Click Here to Learn More. )
Index
- ACNP
- Aerospace Database
- BASE (Bielefeld Academic Search Engine)
- CNKI Scholar
- COPAC
- DTU Library
- Elektronische Zeitschriftenbibliothek (EZB)
- EuroPub Database
- Excellence in Research for Australia (ERA)
- Google Scholar
- Harvard Library
- Infotrieve
- JournalTOCs
- LOCKSS
- MIAR
- Mir@bel
- PKP Open Archives Harvester
- Publons
- ResearchGate
- SHERPA/RoMEO
- Standard Periodical Directory
- Technische Informationsbibliothek (TIB)
- UCR Library
- WorldCat
Contact
- Wendy SmithEditorial Assistant
- ijsp@ccsenet.org