FINITE TIME STABILITY AND OPTIMAL CONTROL OF A STOCHASTIC REACTION DIFFUSION ECHINOCOCCOSIS MODEL WITH IMPULSE AND TIME-VARYING DELAY

This paper presents a model for echinococcosis which incorporates stochastic reaction diffusion, impulse, and time-varying delay. First, the existence and uniqueness of global positive solution is proved through the construction of a Lyapunov function. Then, by applying the bounded impulse interval method, several sufficient conditions for finite time stability (FTS) are obtained. Finally, from the angle of cost-benefit, the issue of optimal control of echinococcosis is presented with the aim of minimizing infection and controlling costs. The validity of the analytical results is verified by numerical simulations.