Time delay in non-lethal infectious diseases

DOI: 10.4236/ns.2012.48075   PDF   HTML   XML   4,216 Downloads   6,174 Views  


The effects of the incubation period q on the dynamics of non-lethal infectious diseases in a fixed-size population are studied by means of a delay differential equation model. It is noted that the ratio between the quantity q and the time τ for recovering from the illness plays an important role in the onset of the epidemic breakthrough. An approximate analytic expression for the solution of the delay differential equation governing the dynamics of the system is proposed and a comparison is made with the classical SEIR model.

Share and Cite:

Luca, R. (2012) Time delay in non-lethal infectious diseases. Natural Science, 4, 562-568. doi: 10.4236/ns.2012.48075.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Anderson, R.M. and May, R.M. (1979) Population biology of infectious diseases: Part I. Nature, 280, 361-367. doi:10.1038/280361a0
[2] Anderson, R.M. and May, R.M. (1979) Population biology of infectious diseases: Part II. Nature, 280, 455-461. doi:10.1038/280361a0
[3] Hyman, J.M., J. Li and Stanley, E.A. (1999) The differential infectivity and staged progression models for the transmission of HIV. Mathematical Bioscience, 155, 77-109. doi:10.1016/S0025-5564(98)10057-3
[4] Li, M.Y., Graef, J.R., Wang, L. and Karsai, J. (1999) Global dynamics of a SEIR model with varying total population size. Mathematical Bioscience, 160, 191-213. doi:10.1016/S0025-5564(99)00030-9
[5] Lipshitch, M.M., Cohen, T., Cooper, B., Robins, J.M., Ma, S., James, L., Gopa-lakrishna, G., Chew, S.K., Tan, C.C., Samore, M.H., Fisman, D. and Murray, M. (2003) Transmission dynamics of Severe Acute Respiratory Syndrome. Science, 300, 1966-1970. doi:10.1126/science.1086616
[6] Hethcote, M. (2000) The mathematics of infectious diseases. SIAM Review, 42, 599-653. doi:10.1137/S0036144500371907
[7] Noviello, A., Romeo, F. and De Luca, R. (2006) Time Evolution of non-lethal infectious diseases: A semi-continuous approach. European Physical Journal B, 50, 505-511. doi:10.1140/epjb/e2006-00163-4

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.