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(a) Backward bifurcation ((0.81leqalphaleq0.86)).
The proposed model may possess a backward bifurcation.
The authors also examined the phenomenon of backward bifurcation.
When we choose appropriate parameters, there exists a backward bifurcation.
Therefore, (3) does not have the bistable dynamics even though a backward bifurcation occurs.
The results reveal that backward bifurcation could occur for a reasonable set of parameter values.
The authors found that the model can produce backward bifurcation and complex dynamics.
Moreover, we prove the existence of a backward bifurcation around the disease-free equilibrium.
It is shown that the backward bifurcation phenomenon is caused by the malaria-induced mortality in humans.
It is shown that the re-infection of birds infected with the LPAI strain causes the backward bifurcation phenomenon.
The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models.
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