Stochastic Asymptotic Stability of SIR Model with Variable Diffusion Rates

摘要: We introduce random fluctuations on contact and recovery rates in deterministic SIR model with disease deaths nonparametric manner obtain stochastic counterparts general diffusion coefficients (functional rates). $$\begin{aligned} \displaystyle dS&= \,\Big (-\beta S I +\mu (K-S)\Big )~dt - I~ F_1\big (S,I,R\big ) ~dW_1\nonumber \\ dI&= (\beta I-\big (\alpha +\gamma \big )I\Big )~ dt + ~dW_1-I~F_2\big ~dW_2 dR&= \mu R\Big )~dt+ I~F_2\big ~dW_2. \nonumber \end{aligned}$$ (1) The introduced has functional which contains arbitrary local Lipschitz-continuous functions \(F_i\)’s defined {\mathbb {D}}=\{(S,I,R) \in {R}}^3: ~S\ge 0, ~I \ge ~R ~S+I+R\le K\}. \end{aligned}$$ In this paper we prove the global existence of a unique strong solution discuss asymptotic stability free endemic equilibria visualize our results some simulations to confirm them.