Epidemic model

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

EIR system

In the modeling transmission dynamics of a communicable disease, it is common to dividethe population into disjoint classes (compartments) whose sizes change with time.The infection status of any individual in a population can be Susceptible, when theperson is healthy and susceptible to the disease (denoted by S), Exposed, when theperson is in a latent period but not yet infectious (denoted by E), Infected, whenthe individual carries the disease and is infectious (denoted by I), or Removed, whenthe person has recovered and is at least temporarily immune or has died because ofdisease (denoted by R). In some diseases such as HIV, there is no recovery. In otherdiseases, 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 withimmunity. 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 immunityand in cases where there is no immunity, models are named SIS or SEIS. The last Spoints the individual becoming susceptible again, after recovery. Such models maybe 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 [Z. Liu, Y.C. Lai, N. Ye, Phys. Rev. E 67 (2003) 031911.] and SARS [S. Riley, et al., Science 300 (2003) 1961.] [M. Lipsitch, et al., Science 300 (2003) 1966.] and even for the spread of rumors [D.H. Zanette, Phys. Rev. E 64 (2001) 050901(R).] [D.H. Zanette, Phys. Rev. E 65 (2002) 041908.] . 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. [K. Dietz, K.P. Hadeler, Epidemiological models for sexually transmitted diseases. Journal of mathematical biology, 26, 1-25, (1988)] 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