Share This Article:

Time delay in non-lethal infectious diseases

Full-Text HTML XML Download Download as PDF (Size:294KB) PP. 562-568
DOI: 10.4236/ns.2012.48075    3,728 Downloads   5,595 Views  
Author(s)    Leave a comment


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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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


[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 © 2018 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.