## Population size

As mentioned above, the continuation of an epidemic is determined by the number of susceptibles remaining in the population.

Fig. 2.6. Basic reproductive rate increasing - i.e. >1. Maximal transmission: every infection produces a new case.

Case reproductive rate = 2

Fig. 2.6. Basic reproductive rate increasing - i.e. >1. Maximal transmission: every infection produces a new case.

Basic reproductive rate = 0.66

Fig. 2.7. Basic reproductive rate decreasing- i.e. <1. Unsustained transmission: each transmission gives rise to less than one new case and the infection dies out.

Once an individual has experienced an episode of the disease (whether manifest or not), he or she may develop immunity (either temporary or permanent) or die. When a certain number of individuals have developed immunity then there are insufficient susceptibles and the infection dies out. This collective permanent immunity (as occuring in viral infections) is called the herd immunity. After a period of time, depending on the size of the population, this herd immunity becomes diluted by new individuals born (or by immigration) and a new epidemic can take place. This is called the critical population (the theoretical minimum host population size required to maintain an infecting agent). It depends upon the infectious agent, the demographic structure and the conditions (hygiene, etc.) of the host population. In third world countries with their high birth rates the critical population is less than that in developed countries. Examples of the critical human population size are for measles 500,000 and for varicella 10,000.

If the population is less than the critical size, then regular epidemics will occur at intervals related to the population size. An example is given in Fig. 12.2 of a measles epidemic, which occurred regularly every 3 years in a well-defined community. These regular epidemics can be analysed in the same way as a propagated source epidemic, from which it has been shown that the smaller the community, the longer is the interval between epidemics.

An extension of the concept of herd immunity shows that not everyone in a population needs to be vaccinated to prevent an epidemic. On the same principle as calculating the critical population, the critical rate of vaccination coverage can also be worked out. In other words, the population that will need to be successfully vaccinated to reduce the population at risk below the epidemic threshold. It can be similarly shown that even if this target is not reached, then the epidemic will be put off until a future date when the susceptible unvaccinated children will have grown older and therefore be able to cope with the infection better. This is illustrated in Fig. 12.2.

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