WWW.WAS.ORG • WORLD AQUACULTURE • MARCH 2013 61 (CONTINUED ON PAGE 62) potential of disease transmission to occur. In experimentally initiated epidemics of infectious pancreatic necrosis (IPN) in rainbow-trout fry, transmissibility was inversely related to the initial density of susceptible hosts (Smith et al. 2000). Fish density, number of infectious fish and the interaction between these two variables significantly affects survival of rainbow trout fry during experimentally induced epidemics of IPN (BebakWilliams et al. (2002). Density dependence in fish diseases is also documented in experimental studies that observed transmission dynamics of furunculosis in chinook salmon (Ogut et al. 2005) and the spread of infectious hematopoietic necrosis virus (IHNV) in rainbow trout (Ogut and Reno 2004). Mardones et al. (2011) estimated the R0 for infectious salmon anemia to be in the range of 1.3 to 2.5. R0 can be estimated with information from field or experimental studies. One limitation of field studies is identification of the specific time when an infected individual is first introduced into a naive population. Lack of this knowledge makes it very difficult or impossible to observe the epidemic of disease during the early introduction phase. Experimental studies might not adequately represent what is happening in the field. Mathematical models can be used to describe the behavior of infectious diseases and the effect of control measures over time. The simplest model subdivides a population into mutually exclusive subgroups, such as 1) a group of individuals (S) that are susceptible to the infection, 2) a group of infectious individuals (I) that are infected and able to transmit the infection, and 3) a group of resistant individuals (R) that are recovered from being infected and are no longer infectious. Although vaccination cannot, in general, be considered to be a preventive measure that completely eliminates the risk of infection of a population with a specific pathogen, the protection achieved may significantly reduce the number of susceptible individuals. The resulting herd immunity may effectively prevent an infection from becoming established and spread within a population and to other aquaculture installations. TABLE 1. R0 represents the average number of secondary infected individuals arising from a single primary infected individual. DISEASE POPULATION R0 HERD IMMUNITY REFERENCE THRESHOLD (%) Foot-and-mouth Cattle 3.5-4.5 71-78 Ferguson et al. 2001 Disease Rabies Dogs 2.4 59 Kitala et al. 2002 Highly Pathogenic Poultry 1.9-2.6 47-62 Ward et al. 2009 Avian Influenza (H5N1) Tuberculosis Cattle 2.6 61 Godchild and Clifton- Hadley 2001 Infectious Salmon Atlantic 1.3-2.5 23-60 Mardones et al. 2010 Anemia (ISA) salmon farm FIGURE 1. Dynamics of sub-populations in a non-vaccinated fish population after an introduction of an infectious fish with a disease with an R0 of 3. S is the subpopulation of susceptible individuals, I is the subpopulation of infectious individuals, D is the subpopulation of dead individuals.
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