Sentence examples for conditions for persistence from inspiring English sources

Then, several conditions for persistence in mean and extinction of the disease are also established.

Moreover, the sufficient conditions for persistence in mean, extinction are obtained.

Theorem 2.1 describes sufficient conditions for persistence in the mean and extinction, which are derived from the stochastic analysis theory.

Unfortunately, conditions for persistence are poorly characterized, as are the larval dispersal patterns on which persistence depends.

end{cases} (3) In model (3), the authors discussed in detail the conditions for persistence in mean and extinction of each epidemic disease.

Further, the conditions for persistence and extinction of the disease are also established, where a threshold is given in the case that the noise is small.

These models allow us to examine analytically the effects of spatial structure in habitat loss on the equilibrium metapopulation size and the threshold condition for persistence.

These quantities include the threshold condition for persistence, the contributions that individual habitat patches make to metapopulation dynamics and persistence, the time to metapopulation extinction, and the effective size of a metapopulation living in a heterogeneous patch network.

However, such mutual invasibility is a condition for persistence.

Besides, sufficient conditions for extinction, persistence in mean, and weak persistence are obtained.

In this case, all the conditions required for persistence are violated.