About GAIA GAIA Case Studies Global GIS Agenda 21 Country Data Model Database

Evaluating the role of exogenous reinfection

The debate over the epidemiological importance of the exogenous reinfection has not yet concluded. Such type of infection has been confirmed both for patients with immunocompetent (Raleigh and Wichelhausen, 1973; Raleigh et al, 1975; Bates et al, 1976) and for those with immunosuppression (Nardell et al, 1986; Small et al, 1993). Sutherland et al. (1976, 1982) compared the relative epidemiological importance of such type of infection compared to the primary infection and the endogenous reactivation. These researchers concluded that the exogenous reinfection cannot be excluded when the dynamics of tuberculosis is analyzed at the population level. Nevertheless, Blower et al. (1995) have explicitly ignored it when developing their model of transmission of tuberculosis because they considered that it only occurs in areas with high incidence or between indviduals with immunological difficiences. It is clear to us that ignoring the exogenous reinfection would not be appropiate for developing countries where the incidence rates are high ( over 100/100,000 ), particularly in Africa, where the seroprevalence with HIV is also high (Snider et al, 1994). It is important to consider that the dynamics of tuberculosis in the developed countries could also be affected by such reinfection. In the more poor areas of big cities, the rates of incidence can be very high, for example in Central Harlem (in New York City -U.S.A.) the incidence of tuberculosis is of 160 individuals of 100,000, matching a high rate of seroprevalence of HIV and a high concentration of immigrants of countries with high incidence of tuberculosis. These factores force us to conclude that the rol of exogenous reinfection must be taken into account in the development of population models of the TB dynamics in developed and developing countries.

Castillo-Chavez et al. (1996) developed a model to evaluate the consequences of such reinfection at the population level. The model is defined by the following system of differential equations:

 

In this system of equations, the term  represents the rate of exogenous reinfection. When p = 0, the system is reduced to the basic model (section III a).
The basic reproductive number is:

where  represents the average number of susceptibles infected by an infectious, during his infectious period, and,  represents the fraction of the population that survives the latent period (D E ). Therefore Ro denotes the total number of infectious secondary cases produced by an infectious individual during his infectious period.

It is important to highlight that Ro does not depend on the parameter p, and it is essentially the same that for the model without reinfection. With  the qualitative behavior of the system shows us that there is an endemic equilibrium point, asymptotically stable, different from zero. Nevertheless, Castillo-Chavez et al (1996) have showed that there is a region of valued of p, where the system when  can maintain multiple endemic equilibria. Essentially, they have shown that for all  there are positive equilibrium points (endemics) when  , where:

where

The results of this model show that there are endemic equilibria even when  . This would explain how the input of infectious individuals to a population can cause an epidemic peak that would stabilize in an endemic level that would not have been possible with the same parameters if there were no exogenous reinfection. Immigrants of countries with high incidence rates that settle in poor areas of big cities could cause epidemic outbreaks that would finally settle as endemics. This in turn could be favored by malnutrition or problems derived from alchohol or drug abuse that generally are associated to such marginal areas of the big cities.

References

Bates, J. H., Stead, W. , Rado, T. A. (1976). Phage type of tubercle bacilli isolated from patients with two or more sites of organ involvement. Am. Rev. Respir. Dis. 114: 353-8.

Blower, S. M., McLean , A. R., Porco, T. C., Small, P. M., Hopwell, P. C., Sanchez, M. A., Moss, A. R. (1995). The intrinsic transmition dynamics of tuberculosis epidemics. Nature Medicine 1(8): 815-821.

Castillo-Chavez, C., Feng, Z., Capurro, A.F. (1997) A TB Model with Exogenous Reinfection . Biometric Unit - Technical Report BU-1388-M, Cornell University, Ithaca, NY, USA.

Nardell, E. , Mc Innis, B, Thomas, B., Weidhaas, S. (1986). Exogenous reinfection with tuberculosis in a shelter for the homeless. N. Engl. J. Med. 315: 1570-5.

Raleigh, J. W, Wichelhausen, R. H., Rado, T. A. , Bates, J. H. (1975). Evidence for infection by two distinct strains of Mycobacterium tuberculosis in pulmonary tuberculosis: report of 9 cases. Am. Rev. Respir. Dis. 112: 497-503.

Raleigh, J. W. , Wichelhausen, R. H. (1973). Exogenous reinfection with Mycobacterium tuberculosis confirmed by phage typing. Am. Rev. Respir. Dis. 108: 639-42.

Small, P.M., Shafer, R. W., Hopewell, P.C., Singh, S.P., Murphy, M. J., Desmond, E, Sierra, M.F., Schoolnik, G.K. (1993). Exogenous reinfection with multidrug-resistant Mycobacterium tuberculosis in patients with advanced HIV infection. N. Engl. J. Med. 328: 1137-44.

Snider, D. E., Raviglione, M., Kochi, A.(1994) Global Burden of tuberculosis. In: Bloom, B.R. (Ed.): Tuberculosis: Pathogenesis, Protection and Control, pp 3-12, ASM Press, Washington .

Sutherland, I, Svandova, E, Radhakrishna, S. (1982) The development of clinical tuberculosis following infection with tubercle bacilli. 1. A theoretical model for the development of clinical tuberculosis following infection, linking from data on the risk of tuberculosis infection and the incidence of clinical tuberculosis in the Netherlands. Tubercle 63: 255-68.

Sutherland, I. (1976) Recent studies in the epidemiology of tuberculosis, based on the risk of being infected with tubercle bacilli. Adv. Tuberc. Res. 19: 1- 63.

Raleigh, J. W. , Wichelhausen, R. H. (1973). Exogenous reinfection with Mycobacterium tuberculosis confirmed by phage typing. Am. Rev. Respir. Dis. 108: 639-42.

Raleigh, J. W, Wichelhausen, R. H., Rado, T. A. , Bates, J. H. (1975). Evidence for infection by two distinct strains of Mycobacterium tuberculosis in pulmonary tuberculosis: report of 9 cases. Am. Rev. Respir. Dis. 112: 497-503.

 

Go to run Model


Copyright 1995-2000 by:   ESS   Environmental Software and Services GmbH AUSTRIA