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Modeling Cholera Epidemiology Using Stochastic Differential Equations

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  • Wahab A. Iddrisu
  • Inusah Iddrisu
  • Abdul-Karim Iddrisu

Abstract

In this study, we extend Codeço’s classical SI‐B epidemic and endemic model from a deterministic framework into a stochastic framework. Then, we formulated it as a stochastic differential equation for the number of infectious individuals I(t) under the role of the aquatic environment. We also proved that this stochastic differential equation (SDE) exists and is unique. The reproduction number, R0, was derived for the deterministic model, and qualitative features such as the positivity and invariant region of the solution, the two equilibrium points (disease‐free and endemic equilibrium), and stabilities were studied to ensure the biological meaningfulness of the model. Numerical simulations were also carried out for the stochastic differential equation (SDE) model by utilizing the Euler‐Maruyama numerical method. The method was used to simulate the sample path of the SI‐B stochastic differential equation for the number of infectious individuals I(t), and the findings showed that the sample path or trajectory of the stochastic differential equation for the number of infectious individuals I(t) is continuous but not differentiable and that the SI‐B stochastic differential equation model for the number of infectious individuals I(t) fluctuates inside the solution of the SI‐B ordinary differential equation model. Another significant feature of our proposed SDE model is its simplicity.

Suggested Citation

  • Wahab A. Iddrisu & Inusah Iddrisu & Abdul-Karim Iddrisu, 2023. "Modeling Cholera Epidemiology Using Stochastic Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnljam:v:2023:y:2023:i:1:n:7232395
    DOI: 10.1155/2023/7232395
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    References listed on IDEAS

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    1. Nicholas Kwasi-Do Ohene Opoku & Cecilia Afriyie, 2020. "The Role of Control Measures and the Environment in the Transmission Dynamics of Cholera," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-16, February.
    2. Kinfe Hailemariam Hntsa & Berhe Nerea Kahsay, 2020. "Analysis of Cholera Epidemic Controlling Using Mathematical Modeling," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2020, pages 1-13, August.
    3. Greenhalgh, D. & Liang, Y. & Mao, X., 2016. "SDE SIS epidemic model with demographic stochasticity and varying population size," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 218-238.
    4. Nicholas Kwasi-Do Ohene Opoku & Cecilia Afriyie, 2020. "The Role of Control Measures and the Environment in the Transmission Dynamics of Cholera," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
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