Persistence and extinction of a stochastic AIDS model driven by Lévy jumps

This paper studied a stochastic AIDS model driven by Lévy jumps. We obtained the sufficient conditions for persistence in the mean and extinction. If the modified basic reproduction number R ¯ > 1 , AIDS is persistent in the mean. If the modified basic reproduction number R ~ < 1 , AIDS will die out. In addition, we find that the smaller the transmission coefficient β i , the faster the disease dies out by numerical simulations. We can conclude that it is possible to reduce the risk of epidemic disease transmission by reduce the transmission coefficient β i of epidemic disease.