Bulletin of Mathematical Biology (2022) 84:41 https://doi.org/10.1007/s11538-022-01001-x ORIGINAL ARTICLE A Comparison of Deterministic and Stochastic Plant-Vector-Virus Models Based on Probability of Disease Extinction and Outbreak Sunil Maity 1 · Partha Sarathi Mandal 1 Received: 3 September 2021 / Accepted: 24 January 2022 © The Author(s), under exclusive licence to Society for Mathematical Biology 2022 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 analyt- ically 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 calcu- lated 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. Keywords Cassava mosaic disease · Stochastic model · Markov chain · Multitype branching process · Probability of extinction 1 Introduction Plants are essential for both humans and many other creatures. They are sources of food, medicine, clothing fibre, and housing materials. They are an essential part of maintaining a healthy ecosystem. Plant viruses are one of the most important obstacles to modern agriculture, especially in lesser-developed countries, and are often spread by insects (Hebert and Allen 2016; Jeger et al. 2004; Thresh 1983; Waterworth and Hadidi 1998; Fereres et al. 2000). Begomoviruses, which are carried by the whitefly Bemisia B Partha Sarathi Mandal parthas@nitp.ac.in 1 Department of Mathematics, NIT Patna, Patna, Bihar, India 0123456789().: V,-vol 123