## Transmission Dynamics

Beginning in the early 1970s, mathematicians Herbert Hethcote and James Yorke constructed a theoretical framework for the transmission dynamics of gonorrhea. Using some of the concepts of population ecology, they noted that the reproduction rate for gonorrhea (i.e., the ability of an infected person to replace him- or herself) must be determined when the disease is at endemic equilibrium. In the steady state, therefore, each infected person must have two "adequate" contacts for transmission on average ("adequate" means that the gonococcus is transmitted). There must be a "source" contact and a "spread" contact for disease propagation. Because not all sexual contacts are "adequate," it follows that the average number of total contacts must be greater than 2.

In constructing a model of transmission dynamics, several key epidemiological observations must be considered:

1. Gonococcal infection does not confer protective immunity; thus an individual is "immune" only when infected.

2. Individuals become infectious soon after exposure; there is, then, no "exposed, incubating" group to be considered in a model.

3. Seasonal variation of gonorrhea is well defined, with a peak in late summer in temperate climates, but the variation is small (about 10 percent) in comparison with other diseases. This implies that the parameters used in the model can be constant.

4. Data derived from interviewing gonorrhea patients about their sex partners suggest that the average number of "adequate" contacts is well below 2. In 1985, there were only 0.3 infected contacts found for each person with gonorrhea interviewed. Even with allowances for slippage in the system of interviewing cases, finding contacts, and bringing them to medical examination, this is far below the two infected contacts per case needed to maintain a reproduction rate of 1 and to preserve endemic equilibrium.

It was reasoned, then, that the observed number of infected contacts per case is a weight average of two groups: (1) those for whom one or no contacts were identified (nontransmitters); (2) those with two or more contacts identified (transmitters). Those in the first group - the vast majority of gonorrhea infectees - were unlikely to pass the infection to another person. Hethcote and Yorke hypothesized that the transmitters - those who actually main tain the endemicity of gonorrhea - were drawn from so-called core groups. These groups were defined as persons with stable sociodemographic and geographic characteristics who constituted a small minority of cases (under 5 percent), but who accounted - either directly or indirectly - for most gonorrhea transmission. It is within such groups that the epidemiological features of gonorrhea (no immunity, immediate infectiousness, year-round transmission) were fully operative. The limit to gonorrhea spread within a core group was termed the saturation effect: that is, sexual contact between infected persons.

In a series of elegant mathematical discussions, Hethcote and Yorke developed a model for the dynamics of transmission based on population compartments that included core and noncore groups. They were able to demonstrate the plausibility of an equilibrium state in which most cases were attributable to small groups of active transmitters. Parallel with this theoretical development, some empirical evidence for the physical existence of core geographic areas and definable core groups emerged.

It was shown in 1979, based on the routine reporting of gonorrhea morbidity data, that the city of Denver contained four different areas with high concentrations of infectees (see Figure VIII.62.4). Each geographic area housed a distinct population subgroup: black heterosexuals, Hispanic heterosexuals, white homosexual men, and military recruits.

Through analysis of over 120,000 geocoded cases

Figure VIII.62.4. Distribution of gonorrhea in Denver, Colorado, 1974-6. [From R. B. Rothenberg. 1979. Analysis of routine data describing morbidity from gonorrhea. Sexually Transmitted Diseases 6(1): 5-9; 6, fig. 1, by courtesy of Lippincott/Harper & Row, Philadelphia, Penna.]

of gonorrhea in upstate New York from 1975 to 1980, a general geographic pattern emerged. Within all 12 Standard Metropolitan Statistical Areas (SMSAs, the urban centers), there was intense concentration of gonorrhea in a small number of contiguous census tracts (core areas) within the inner cities. In a concentric circle surrounding the core were a group of census tracts with somewhat lessened gonorrhea rates (adjacent areas). The rest of the SMSA constitutes the peripheral area, with a markedly diminished gonorrhea burden. The concentration of gonorrhea in the core area was 20-fold higher than that for New York State in general, and several of the census tracts in the core had rates that were 40-fold higher. Not only was this pattern repeated in all SMSAs, but all the core areas were similarly characterized by high population density and low socioeconomic status. The geographic configuration for Buffalo, New York, is typical (Figure VIII.62.5).

This pattern was also documented in Colorado Springs, Colorado, using data collected from inter views of 97 percent of the cases that occurred during a 6-month interval. Again, clustering of over 50 percent of the cases was demonstrated in about 5 percent of census tracts. Social aggregation of cases was demonstrated by the consistent use of six drinking establishments by a major proportion of infectees, and by the aggregation of patients and their sexual partners in the same census tracts. Contrary to commonly held belief, the majority of sexual partners had known each other socially prior to sexual contact. The interconnection of individuals in networks could be demonstrated through linkage provided by the interview process. Further analysis demonstrated that the core groups in Colorado Springs generated a high force of infectivity (i.e., days of potential transmission in infected exposed partners),

TOTALS PPNG

pen sensitive Total

PPNG % Total

Figure VIII.62.5. Occurrence of gonorrhea in Buffalo, New York, 1975-80; distribution of core and adjacent tracts. (From R. B. Rothenberg. 1983. The geography of gonorrhea: Empirical demonstration of core group transmission. American Journal of Epidemiology 117(6): 688-94; 691, fig. 1.)

TOTALS PPNG

pen sensitive Total

PPNG % Total

Figure VIII.62.6. Penicillinase-producing Neisseria gonorrhea (PPNG) as percentage of total gonorrhea, by zip code analysis in Miami, Florida, March 1985 to February 1986. (From J. M. Zenilman et al. 1988. Penicillinase-producing Neisseria gonorrhoeae in Dade County, Florida: Evidence of core-group transmitters and the impact of illicit antibiotics. Sexually Transmitted Diseases 15: 45-50; 47, fig. 2, by courtesy of Lippincott/Harper & Row, Philadelphia, Penna.)

Figure VIII.62.5. Occurrence of gonorrhea in Buffalo, New York, 1975-80; distribution of core and adjacent tracts. (From R. B. Rothenberg. 1983. The geography of gonorrhea: Empirical demonstration of core group transmission. American Journal of Epidemiology 117(6): 688-94; 691, fig. 1.)

CORE adjacent and had a heightened degree of sexual interaction both inside and outside their core groups.

Similar geographic clustering was documented in Seville, Spain, where it was noted that all the STD syndromes appeared to exhibit a similar geographic pattern. The presence of penicillin-resistant N. gonorrhoeae has provided a convenient marker for the demonstration of core-group aggregation as well. In an initial outbreak reported from Liverpool in 1976, clustering of cases occurred within two small inner-city districts. In Miami, a major endemic area for resistant gonorrhea in the United States, the clustering of resistant cases within presumed core-group areas paralleled that for all of gonorrhea (Figure VIII.62.6).

It cannot be assumed that the geographic characteristics displayed in these examples are universal. In particular, differences in human ecology and sexuality in developing countries may dictate a different pattern, and data are not yet available. It might tentatively be concluded, however, that a concentric pattern of gonorrhea risk, which diminishes outward from the central inner city, exists in many major urban areas. The potential for use of geographic patterns in the development of disease control strategies, and in the understanding of other sexually transmitted syndromes, is an area for further development.

### Richard B. Rothenberg

This chapter was written in the author's private capacity. No official support or endorsement by the Centers for Disease Control is intended or should be inferred.