A method to calculate—for computer-simulated infections—the threshold value, R0, that predicts whether or not the infection will spread

Computer-simulation models of infections can easily incorporate heterogeneity among animals (important for the effect of control measures) by allocating animals to various classes. These classes are termed 'states' and the change from one state to another, during a unit of time, is termed a 'transition'. Hence, most computer models are state-transition models. Using a fairly universal representation of state-transition models, we derived an analytic expression (a formula) for the basic reproduction ratio of infection (R0), i.e. the number of cases caused by one typical infectious animal. When R0 > 1, the infection can spread; when R0 < 1, the infection will disappear. Therefore, a strategy for controlling an infective agent is effective when, and only when, the ratio for that strategy is less than one.Using the reproduction-ratio formula derived in this paper (instead of interpreting results from a large number of simulations) has several advantages for veterinary researchers. The structure of the formula allows investigators to understand how certain parameters (e.g. infection, demographic or control-strategy parameters), if changed, will influence the ratio. Moreover, the ratio can be calculated directly and quickly, hence whether an infection will spread or disappear can be determined quickly. In addition, because certain parameters present in the original model disappear in the formula for the ratio, they can be eliminated as influencing the effectiveness of the control strategy. Finally, the value of R0 can be interpolated for parameter values (e.g. rates of infection, contact rates, replacement rates and herd sizes) other than those evaluated originally.