A Two-strain TB Model With Patchy Environment

A two-strain TB model is established in a two-patch environment, which assumes the drug-susceptible bacteria can change to drug-resistant TB bacteria by mutation.The expressions of basic reproduction number corresponding to each strain as well as invasion reproduction number are obtained, noting as Ro1,Ro2, R21. The existence conditions of the disease-free equilibrium, dominant equilibrium and coexistence-equilibrium are learned. Conclusions are verified which includes that when R0=max{R{Ro1,Ro2}<1, the disease free equilibrium is G.A.S.; When R0>1,R21<1, the dominant equilibrium is L.A.S.; When R21>1, the coexistence-equilibrium is L.A.S.. Besides, if it is unique, it is G.a.s.. Finally, the numerical work is introduced into the paper to check the former results, showing the relations between dispersal rate and the stability of the system.