Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 72, Issue 2, Pages 490-505Publisher
SPRINGER
DOI: 10.1007/s11538-009-9458-y
Keywords
Varying temporary immunity; Epidemic model; Delay differential equations
Categories
Funding
- EPSRC [EP/E045073/1]
- EPSRC [EP/E045073/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/E045073/1] Funding Source: researchfish
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An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is performed using DDE-BIFTOOL and traceDDE to investigate different dynamical regimes in the model using numerical continuation for different values of system parameters and different integral kernels.
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