A continuous time Markov chain model for the dynamics of bovine tuberculosis in humans and cattle

Stephano, Mussa A.; Irunde, Jacob I.; Mwasunda, Joshua A.; Chacha, Chacha S.

doi:10.1007/s11587-022-00696-3

Cited by 3 publications

(2 citation statements)

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“…The probability-generating functions r 1 , r 2 , ⋯, r 6 exhibit nonlinearity, rendering them difficult to compute analytically. 9 Journal of Applied Mathematics Consequently, numerical simulations, as demonstrated by Stephano et al [15], are employed for their computation.…”

Section: Ctmc Stochastic Model Formulationmentioning

confidence: 99%

“…Nevertheless, the existing models did not incorporate stochastic behavior in dynamics. The significance of the CTMC model is that it captures variabilities and uncertainties that arise due to environmental variations and demographics and also predicts the probabilities of extinction or outbreak in finite time and studies the random sample path solutions near disease-free and endemic equilibria [12][13][14][15]. This paper presents a stochastic CTMC model based on the modified existing deterministic models of lymphatic filariasis dynamics.…”

Section: Introductionmentioning

confidence: 99%

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The Significance of Stochastic CTMC Over Deterministic Model in Understanding the Dynamics of Lymphatic Filariasis With Asymptomatic Carriers

Stephano,

Irunde,

Mayengo

et al. 2024

Journal of Applied Mathematics

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Lymphatic filariasis is a leading cause of chronic and irreversible damage to human immunity. This paper presents deterministic and continuous-time Markov chain (CTMC) stochastic models regarding lymphatic filariasis dynamics. To account for randomness and uncertainties in dynamics, the CTMC model was formulated based on deterministic model possible events. A deterministic model’s outputs suggest that disease extinction is feasible when the secondary threshold infection number is below one, while persistence becomes likely when the opposite holds true. Furthermore, the significant contribution of asymptomatic carriers was identified. Results indicate that persistence is more likely to occur when the infection results from asymptomatic, acutely infected, or infectious mosquitoes. Consequently, the CTMC stochastic model is essential in capturing variabilities, randomness, associated probabilities, and validity across different scales, whereas oversimplification and unpredictability of inherent may not be featured in a deterministic model.

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Section: Ctmc Stochastic Model Formulationmentioning

confidence: 99%