Epidemic model

An Epidemic model is a simplified means of describing the transmission of communicable disease through individuals.

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SEIR system

In the modeling transmission dynamics of a communicable disease, it is common to divide the population into disjoint classes (compartments) whose sizes change with time. The infection status of any individual in a population can be Susceptible, when the person is healthy and susceptible to the disease (denoted by S), Exposed, when the person is in a latent period but not yet infectious (denoted by E), Infected, when the individual carries the disease and is infectious (denoted by I), or Removed, when the person has recovered and is at least temporarily immune or has died because of disease (denoted by R). In some diseases such as HIV, there is no recovery. In other diseases, if an infected person recovered he/she may be susceptible again.

A sequence of letters, such as SEIR, describes the movement of individuals between the classes: susceptibles become latent, then infectious and finally recover with immunity. To model diseases which confer permanent immunity and which are endemic because of births of new susceptibles, SIR or SEIR models with vital dynamics are suitable. Vital dynamics is needed to avoid explosion of the population size. Models of SEIRS or SIRS types are used to model diseases with temporary immunity and in cases where there is no immunity, models are named SIS or SEIS. The last S points the individual becoming susceptible again, after recovery. Such models may be appropriate for gonorrhea, for instance.

Use of models

Epidemic models has been widely used in different forms for studying epidemiological processes such as the spread of influenza [1] and SARS [2,3] and even for the spread of rumors [4,5]. Epidemic models are also applied to modeling of STI epidemics, but not all epidemic models are suitable for STIs since the sexual network plays an important role in spread of disease.

Pair-Formation modeling

Pair-formation models are a type of ordinary differential equation models that have sometimes been used to study STI transmission in populations. They incorporate the repeated contacts within partnerships which happen frequently in real sexual networks. They were first developed in 1988 by Dietz et al. [6] to study STIs in monogamous partnerships. In this model if two susceptible individuals form a pair then they can be considered temporarily immune as long as they do not separate and have no contacts with other partners. This aspect influences transmission dynamics considerably, especially when the disease is first introduced, since the vast majority of existing pairs are susceptible.

References

[1] Z. Liu, Y.C. Lai, N. Ye, Phys. Rev. E 67 (2003) 031911.

[2] S. Riley, et al., Science 300 (2003) 1961.

[3] M. Lipsitch, et al., Science 300 (2003) 1966.

[4] D.H. Zanette, Phys. Rev. E 64 (2001) 050901(R).

[5] D.H. Zanette, Phys. Rev. E 65 (2002) 041908.

[6] K. Dietz, K.P. Hadeler, Epidemiological models for sexually transmitted diseases. Journal of mathematical biology, 26, 1-25, (1988)