Abstract:
A new deterministic model for the transmission dynamics of two strains of in-
uenza is designed and used to qualitatively assess the role of cross-immunity on
the transmission process. It is shown that incomplete cross-immunity could in-
duce the phenomenon of backward bifurcation when the associated reproduction
number is less than unity. The model undergoes competitive exclusion (where
Strain i drives out Strain j to extinction whenever R0i > 1 > R0j ; i; j =
1; 2; i ̸= j). For the case where infection with one strain confers complete im-
munity against infection with the other strain, it is shown that the disease-free
equilibrium of the model is globally-asymptotically stable whenever the repro-
duction number is less than unity. In the absence of cross-immunity, the model
can have a continuum of co-existence endemic equilibria (which is shown to be
globally-asymptotically stable for a special case). When infection with one strain
confers incomplete immunity against the other. Numerical simulations of the
model show that the two strains co-exist, with Strain i dominating (but not
driving out Strain j), whenever R0i > R0j > 1.
