Journal
ADVANCES IN DIFFERENCE EQUATIONS
Volume -, Issue -, Pages -Publisher
SPRINGER
DOI: 10.1186/s13662-018-1805-6
Keywords
SEIR epidemic model; Time delay; Standard incidence; Hopf bifurcation
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Funding
- King Mongkut's University of Technology North Bangkok
- Health Systems Research Institute under the National Science and Technology Agency (NSTDA), Thailand
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In this paper, we analyze a delayed SEIR epidemic model in which the latent and infected states are infective. The model has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number R-C, is less than or equal to unity. We investigate the effect of the time delay on the stability of endemic equilibrium when R-0 > 1. We give criteria that ensure that endemic equilibrium is asymptotically stable for all time delays and a Hopf bifurcation occurs as time delay exceeds the critical value. We give formulae for the direction of Hopf bifurcations and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold reduction for functional differential equations. Numerical simulations are presented to illustrate the analytical results.
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