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A Comparison of Deterministic and Stochastic Plant-Vector-Virus Models Based on Probability of Disease Extinction and Outbreak

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Abstract

In this investigation, we formulate and analyse a stochastic epidemic model using the continuous-time Markov chain model for the propagation of a vector-borne cassava mosaic disease in a single population. The stochastic model is based upon a pre-existing deterministic plant-vector-virus model. To see how demographic stochasticity affects the vector-borne cassava mosaic disease dynamics, we compare the disease dynamics of both deterministic and stochastic models through disease extinction process. The probability of disease extinction and therefore the major outbreak are estimated analytically using the multitype Galton–Watson branching process (GWbp) approximation. Also, we have found the approximate probabilities of disease extinction numerically based on 30000 sample paths, and it is shown to be good estimate with the calculated probabilities from GWbp approximation. In particular, it is observed that there is a very high probability of disease extinction when the disease is introduced via the infected vectors rather than through infected plants.

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Acknowledgements

Sunil Maity’s research is supported by research fellowship from MHRD, Government of India, Partha Sarathi Mandal’s research is supported by MATRICS Project, DST, SERB, India [File No:MTR/2019/000317].

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  1. Department of Mathematics, NIT Patna, Patna, Bihar, India

    Sunil Maity & Partha Sarathi Mandal

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  1. Sunil Maity
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  2. Partha Sarathi Mandal
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Correspondence to Partha Sarathi Mandal.

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Maity, S., Mandal, P.S. A Comparison of Deterministic and Stochastic Plant-Vector-Virus Models Based on Probability of Disease Extinction and Outbreak. Bull Math Biol 84, 41 (2022). https://doi.org/10.1007/s11538-022-01001-x

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