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Based on the deterministic network infectious disease model, a stochastic network infectious disease model under the influence of white noise was established, and the existence and uniqueness of the global solution to the model were proved. With the theory of stochastic differential equations, sufficient conditions for stochastic extinction and persistence of infectious diseases were obtained. The results show that, white noise has a great impact on the transmission dynamics of network infectious diseases. White noise can effectively suppress the spread of infectious diseases, and large white noise can even make the original persistent infectious diseases become extinct. Finally, the theoretical results were verified through numerical simulations. [ABSTRACT FROM AUTHOR]

The dynamic behavior of a stochastic predator-prey model with the Gilpin-Ayala growth was studied. The existence and uniqueness of the global positive solution to the system were proved, and sufficient conditions for system extinction and persistence were obtained. On this basis, the thresholds for controlling the stochastic persistence and extinction of the predator-prey system were given, and some asymptotic behaviors of the solution were discussed. Finally, the effectiveness of the results was verified through numerical simulation. [ABSTRACT FROM AUTHOR]

A modified Euler-Maruyama ( EM) scheme was constructed for a class of multi-term fractional non-linear stochastic differential equations with weak singularity kernels, and the strong convergence of this modified EM scheme was proved. Specifically, according to the sufficient condition for stochastic integral decomposition, the multi-term fractional stochastic differential equation was equivalently transformed into the stochastic Volterra integral equation, and then the corresponding modified EM scheme and its strong convergence were derived and proved, respectively. The order of strong convergence is an, - αm - αm-1 where αi is the index of fractional derivative satisfying 0 < α1, < ... < αm-1 <α1 <1. Finally, numerical experiments verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

The research on population dynamics and related control problems is not only of theoretical significance, but also closely related to biodiversity protection, pest control, and the development and utilization of renewable resources. The optimal harvesting problem was considered in a periodic 3-species predator-prey system with 1 predator and 2 competing preys, where the predator has size structure and was described with 1st-order partial differential equations. First, the existence of a unique non-negative solution of the controlled system was proven by means of the fixed-point reasoning, and the continuous dependence of the solution on the control variables was discussed. Then, the optimal harvesting conditions were given with the techniques of tangential-normal cones and the adjoint system. Finally, with Ekeland's variational principle, the existence of the optimal harvesting strategy was derived. Here the objective functional represents the net economic benefit in the harvesting of 3 species. The results obtained would be beneficial for exploration of renewable resources. [ABSTRACT FROM AUTHOR]