This paper uses regression and simulation to develop some stochastic models of time to completion of development (TTCOD) of a parasite of sheep on pasture under the influence of temperature in the presence of adequate moisture. A statistical distribution is fitted to the development of the parasite at the prevalent average temperature for the day. Approximate solutions using Newton–Raphson method, and MLE estimates were obtained for parameters, and Monte Carlo methods were used to simulate the distributions of development of the parasite at constant and varying temperatures, tracking the stochasticity of the completion of development of the parasite on pasture where its infectivity is a menace to livestock and livestock farmers. The simulated distribution provides a tool for predicting infectivity, which can lead to strategies for containing or eliminating infection.