Hopf Bifurcation of an Epidemic Model with Delay.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 27304674.
- Also identified by DOI 10.1371/journal.pone.0157367 and PMC identifier 4909215.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
Abstract
A spatiotemporal epidemic model with nonlinear incidence rate and Neumann boundary conditions is investigated. On the basis of the analysis of eigenvalues of the eigenpolynomial, we derive the conditions of the existence of Hopf bifurcation in one dimension space. By utilizing the normal form theory and the center manifold theorem of partial functional differential equations (PFDs), the properties of bifurcating periodic solutions are analyzed. Moreover, according to numerical simulations, it is found that the periodic solutions can emerge in delayed epidemic model with spatial diffusion, which is consistent with our theoretical results. The obtained results may provide a new viewpoint for the recurrent outbreak of disease.
Medical subject headings
- Algorithms
- Computer Simulation
- Epidemics
- Models, Theoretical