Use of a mathematical model to study the control measures of the cattle tick Boophilus microplus population in New Caledonia.

Boophilus microplus is a common cattle tick of great economic importance in various tropical and subtropical countries like New Caledonia. The proposed model describes the population dynamics of female Boophilus microplus in the absence of resistant ticks. It is a system of six difference equations which can be mathematically analyzed. The analysis of the system shows the great importance of the eigenvalue denoted by lambda1. The population of ticks increases if lambda1 < 1 and decreases if lambda1 > 1. The lambda1 eigenvalue depends, in particular, on the parasitic surviving rate and encounter rate between the larvae and the cows. The treatments decrease the parasitic surviving rate as the agronomic measures decrease the encounter rate. This model permits to quantify the conditions of treatments (or of the efficacy of a vaccine) and of agronomic measures by which the populations are controlled. It shows that the different treatment rhythms and the presence or not of the wild or domestic refuges plays a major role on the dynamics of tick population.