Narrow Results

In this paper, we consider a Hepatitis C model characterized by acute and chronic infections, treatment as a health-protective measure for the chronically infected is proposed, and its effect on the population is further highlighted. The model is perturbed by white noise and we incorporate Lévy jumps as means to depict abrupt fluctuations. We demonstrate the solution’s existence and uniqueness and deduce adequate criteria for the disease’s extinction and persistence. The importance of treatment as a protective strategy is manifested in its ability to eradicate or mitigate the propagation of the disease. We present numerical simulations to demonstrate the theoretical findings we have obtained.

A new non-autonomous predator-prey system with the effect of viruses on the prey is investigated. By using the method of coincidence degree, some sufficient conditions are obtained for the existence of a positive periodic solution. Moreover, with the help of an appropriately chosen Lyapunov function, the global attractivity of the positive periodic solution is discussed. In the end, a numerical simulation is used to illustrate the feasibility of our results.