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Continuous Time Markov Chain Model for Cholera Epidemic Transmission Dynamics

Author

Listed:
  • Yohana Maiga Marwa
  • Isambi Sailon Mbalawata
  • Samuel Mwalili

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.

Suggested Citation

  • Yohana Maiga Marwa & Isambi Sailon Mbalawata & Samuel Mwalili, 2019. "Continuous Time Markov Chain Model for Cholera Epidemic Transmission Dynamics," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(3), pages 1-32, November.
    • Handle: RePEc:ibn:ijspjl:v:8:y:2019:i:3:p:32
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    References listed on IDEAS

    as
    1. Aaron A. King & Edward L. Ionides & Mercedes Pascual & Menno J. Bouma, 2008. "Inapparent infections and cholera dynamics," Nature, Nature, vol. 454(7206), pages 877-880, August.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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