An environmentally-driven two-strain mutualistic coinfection model with coupling transmission in vivo and vitro and humoral immunity

In this paper, a coupling transmission epidemic model with mutualistic two-strain of virus in body and vitro of host is proposed, in which humoral immune response only works for strain 1 due to immunity evasion of mutation. For the within-host subsystem, the global stability of all feasible equilibria with and without environmental influence are discussed. For the between-host subsystem, the basic reproduction number R 0 is obtained. When R 0 < 1 , the disease-free equilibrium is local stable, while the endemic equilibrium is local stable and the disease is uniformly persistent if R 0 > 1 . Meanwhile, backward bifurcation would occur when there exists immune response within host. Finally, numerical examples are provided to illustrate obtained conclusions, by which we find that the mutualism between two strains during co-infection leads to a more persistent disease than single strain, even the basic reproduction number is small than 1 in each single strain.