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This makes the point that R 0 is dependent upon host density. Note that if the para-

site is highly virulent (large α), if recovery is rapid (large γ), or if the parasite trans-

mits poorly between hosts (small β), then a dense population (large NT) is needed

to stop the infection dying out. Equation 11.7 can be elaborated to take in the effect

of an incubation period and post-infection immunity (both of which increase NT)

and “vertical” transmission of the infection whereby a fraction of the offspring of an

infected female are born infected (which lowers NT).

These equations encapsulate two important concepts of epidemiology:

1 that persistence or extinction of an infection is determined by only a few traits of

the host and parasite;

2 that the density of the hosts must exceed some critical threshold to allow the infec-

tion to persist and spread.

We examine two examples of disease persistence in wildlife populations.

Swine fever

An example of the study of epidemiology involves classical swine fever (CSF) in wild

pigs of Pakistan (Hone et al. 1992). This is a viral disease of pigs spread primarily

by close proximity of hosts. The disease is widespread in Europe, Asia, and Central

and South America. Understanding of its epidemiology is relevant in efforts to keep

it out of North America and Australia.

Classical swine fever was introduced to a population from wild boar (Sus scrofa)

in a 45 km^2 forest plantation in Pakistan. The known starting population (all of which

were susceptibles) was 465. One infected animal was released into this population.

After 69 days, 77 deaths had been recorded and it was assumed there were no deaths

of uninfected animals. The regression of cumulative mortality over time provided a

deterministic estimate of the transmission variable βas 0.00099/day. The threshold

population of pigs (NT) below which the disease cannot persist was estimated by

NT=

where αis the mortality rate from infection and γis the recovery rate. Animals were

infective for 15 days over this period. The mortality rate was 0.2 /day and the recov-

ery rate was 1/15 or 0.067/day. Thus NTwas (0.2 +0.067)/0.00099 =270 animals.

The number of secondary infections (RD) is the ratio of the number of suscept-

ibles (S) (in this case the starting population of 465) to the threshold population NT.

Thus:

RD=S/NT=465/270 =1.7

A disease establishes when RDis unity or greater, but this is valid only for the ini-

tial population and not a prediction for persistence.

In general, six pieces of information are required from an epizootic to make pre-

dictions about the transmission of a disease:

1 the initial abundance of hosts;

2 the number of infectives initially involved;

3 the number of deaths during the epizootic;

α+γ

β

182 Chapter 11