Stochastic Analysis of a Plant-Vector-Virus Model with Saturated Incidence Rate

Cassava mosaic disease (CMD), caused by the cassava mosaic virus (CMV) and transmitted primarily by the whitefly Bemisia tabaci, reflects the most severe and widespread viral threat to cassava cultivation. The emergence of CMD with a nonlinear saturated incidence of Holling type II form is stochastically modeled and analyzed in this paper utilizing the continuous-time Markov chain (CTMC) modeling approach. The most significant distinction between deterministic and stochastic models is that the deterministic model predicts disease persistence when the basic reproduction number $R_0>1$ , whereas the stochastic model, characterized by the branching-process threshold $\rho \left(M\right)$ , indicates that disease extinction can still occur in finite time due to random fluctuations, even when $R_0>1$ . The likelihood of disease extinction is determined using the Galton-Watson branching process (GWbp) approximation and compared to the estimated probability obtained from the stochastic model's 10,000 sample paths. This comparison reveals a substantial link between these probabilities. It is found that the disease has a higher probability of extinction when transmission occurs solely through infected vectors, as opposed to transmission through infected plants or both infected plants and vectors. In the stochastic settings, the implicit equation for the mean first passage time is derived to assess the typical time until the first state transition. Additionally, we evaluate both the quasi-stationary distribution of infected individuals and the probability distribution of the epidemic's ultimate size.