Continuous Time Markov Chain Model for Cholera Epidemic Transmission Dynamics

Yohana Maiga Marwa, Isambi Sailon Mbalawata and Samuel Mwalili

International Journal of Statistics and Probability, 2019, vol. 8, issue 3, 32

Abstract: This paper is concern with modeling cholera epidemic. Despite the advances made in understanding this disease and its treatment, cholera continues to be a major public health problem in many countries. Deterministic and stochastic models emerged in modeling of cholera epidemic, in order to understand the mechanism by which cholera disease spread, conditions for cholera disease to have minor and large outbreaks. We formulate a continuous time Markov chain model for cholera epidemic transmission from the deterministic model. The basic reproduction number (R0) and the extinction thresholds of corresponding cholera continuous time Markov chain model are derived under certain assumptions. We find that, the probability of extinction (no outbreak) is 1 if R0 < 1, but less than 1 if R0 > 1. We also carry out numerical simulations using Gillespie algorithm and Runge–Kutta method to generate the sample path of cholera continuous time Markov chain model and the solution of ordinary differential equation respectively. The results show that the sample path of continuous time Markov chain model fluctuates within the solution of the ordinary differential equation.

Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.ccsenet.org/journal/index.php/ijsp/article/download/0/0/39172/40097 (application/pdf)
http://www.ccsenet.org/journal/index.php/ijsp/article/view/0/39172 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ibn:ijspjl:v:8:y:2019:i:3:p:32

Access Statistics for this article

More articles in International Journal of Statistics and Probability from Canadian Center of Science and Education Contact information at EDIRC.
Bibliographic data for series maintained by Canadian Center of Science and Education ().