This paper considers the use of disease resistance genes to control the transmission of infection through an animal population. Transmission is summarised by R0, the basic reproductive ratio of a pathogen. If R0 1.0 a major epidemic can occur, thus a disease control strategy should aim to reduce R0 below 1.0, e.g. by mixing resistant with susceptible wild-type animals. Suppose there is a resistance allele, such that transmission of infection through a population homozygous for this allele will be R02 R01, where R01 describes transmission in the wildtype population. For an otherwise homogeneous population comprising animals of these two groups, R0 is the weighted average of the two sub-populations: R0 = R01ρ+ R02 (1 - ρ), where ρ is the proportion of wildtype animals. If R01 1 and R02 1, the proportions of the two genotypes should be such that R0 ≤ 1, i.e. ρ ≤ (R0 - R02)/(R01 - R02). If R02 = 0, the proportion of resistant animals must be at least 1 - 1/R01. For an n genotype model the requirement is still to have R0 ≤ 1.0. Probabilities of epidemics in genetically mixed populations conditional upon the presence of a single infected animal were derived. The probability of no epidemic is always 1/(R0 + 1). When R0 ≤ 1 the probability of a minor epidemic, which dies out without intervention, is R0/(R0 + 1). When R0 1 the probability of a minor and major epidemics are 1/(R0 + 1) and (R0 - 1)/(R0 + 1). Wherever possible a combination of genotypes should be used to minimise the invasion possibilities of pathogens that have mutated to overcome the effects of specific resistance alleles.
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