Sentence examples for a backward bifurcation from inspiring English sources
(a) Backward bifurcation ((0.81leqalphaleq0.86)).
The proposed model may possess a 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.
Moreover, we prove the existence of a backward bifurcation around the disease-free equilibrium.
Among the interesting dynamical behaviours of the model, numerical simulations show a backward bifurcation which gives a challenge to the designing of effective control measures.
In addition to having a disease-free equilibrium, which is locally asymptotically stable when the basic reproductive number is less than unity, the model exhibits the phenomenon of backward bifurcation where a stable disease-free equilibrium coexists with a stable endemic equilibrium for a certain range of associated reproductive number less than one.
The model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever the associated reproduction number is less than unity.
The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium (DFE) co-exists with one or more stable endemic equilibria when the associated reproduction number is less than unity.
Rigorous qualitative analyzes of the models show that the malaria model with standard incidence rate exhibits the phenomenon of backward bifurcation whenever a certain epidemiological threshold, known as the basic reproduction number, is less than unity.
The resulting delay differential equation model is shown to undergo the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with one or more stable endemic equilibria when the associated reproduction threshold is less than unity.
