The basic reproductive ratio, R v , is defined as the expected number of secondary infections caused by an infective individual upon entering a totally susceptible population [29] [30] [31] . This quantity is not only important in describing the infectious power of the disease, but can also can supply information for controlling the spread of the disease [32] . The linear stability of E v0 is governed by the basic reproductive ratio R v . Using the next-generation method [31] , we have