Construction of a mathematical Model of early and late Potato Blight based on the stochastic SICR Model

As a devastating fungal disease, that seriously threatens potato production, the transmission process of potato early and late blight is significantly affected by environmental fluctuations. To accurately reveal the epidemic regularity of this disease, a stochastic SICR (Susceptible-Infected-Confined-Recovered) model is a random, epidemiological framework used to analyze disease transmission model for potato early and late blight was constructed in this paper. Through dynamical analysis, first, it was proved that the system has a unique global positive solution, which ensures the biological rationality of the model; second, based on Has'minskii's theory, the sufficient conditions for the existence of the ergodic stationary distribution of the model were derived, clarifying the dynamical mechanism underlying the persistent epidemic of the disease; third, the threshold conditions for disease extinction and persistence in mean were established, identifying the key nodes for disease prevention and control. The results show that when 𝑅0𝑠 > 1, the model has an ergodic stationary distribution and the disease persists in epidemic; when 𝑅 ̅̅0̅<1, the disease will eventually become extinct. This study provides important theoretical support for the risk early warning and precise prevention and control of potato early and late blight.

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