The components of the S–I–R disease model discussed above are dynamic in time (and space). The relative movement of fish from one cohort to another is determined by the efficiency of pathogen transmission.
The so-called ‘‘force of infection,’’ or rate of change of disease in a population, is determined by the following equation: force of infection 5 b 3 I 3 S. (2) In essence, the frequency of contact between an infectious individual (I) and a susceptible individual (S) multiplied by the transmission coefficient (b) will yield the disease incidence.
Although other factors can alter the disease state, this is the prime interaction necessary for the development of epizootics.
The primary component of transmission is the transmission coefficient, b, which is defined as the efficiency of transfer of the pathogen from a single infectious individual to other susceptibles in the population.
This transmission coefficient is independent of the density of individuals and relatesto the probability of infection when one infectious individual transfers, directly or indirectly, a pathogen.
A low b, or inefficient transfer, would probably not result in epizootic disease, whereas a large b will result in an epizootic. Even relatively small changes in b can markedly affect the development of disease (Figure 2). At b 5 1.0, no infection occurs.
Note that a change in b from 1.4 effective contacts per 10,000 fish/d to 2.8 contacts markedly affects not only the incidence of infection but also the time at which the peak infection occurs and the duration of the infection in the population.
Beta, as might be expected, is affected by many factors, the most important of which are summarized in Table 2.
Basic Reproductive Rate R0:
When a pathogen is first introduced into a susceptible population of fish, the process of infectious disease is initiated.
The components of an epizootic can be described as arrival, establishment, spread, and persistence. The rates and intensities of these components can be calculated based on the basic reproductive rate of the pathogen, R0.
The R0 calculation is based on b, the population density, and the duration of infectiousness. Simply expressed, R0 is the number of successful infectious contacts per unit time made by an infective individual in a wholly susceptible population (Mollison 1995a).
Consequently, if R0 is less than 1, either no epizootic will be established (if R0 is low enough) or the disease will die out and the pathogen will be eliminated from the population;
If R0 exceeds 1, an epizootic will occur with the severity dependent on the magnitude of R0. If R0 is slightly above 1, a persistent (enzootic) state of infection will occur with a low prevalence of infected animals in the population.
If R0 for a pathogen is large, it will infect most, if not all, susceptibles and eliminate itself from the population; for example, R0 for measles in humans is approximately 15 (Anderson and May 1982), and it is known that this contagious viral infection is eradicated in a population after an epidemic and only reoccurs with the arrival of new susceptibles, as well as an infectious individual, into the population.
If R0 for a pathogen is low, it will be unable to infect an adequate number of hosts to establish and spread and, thus, will be eradicated; if R0 is near 1, the pathogen will infect a proportion of the susceptibles but not enough to deplete the susceptible population to the point of elimination.
Thus, pathogens that are of intermediate contagiousness tend to persist in populations for long time periods, perhaps indefinitely. Likewise, pathogens that have an intermediate mortality rate will not deplete the population of susceptible so rapidly that the there will not be enough new hosts to infect.
Author:
PAUL W. RENO
