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 importan ce in various tropical and subtropical countries like New Caledonia. T he proposed model describes the population dynamics of female Boophilu s microplus in the absence of resistant ticks. It is a system of six d ifference equations which can be mathematically analyzed. The analysis of the system shows the great importance of the eigenvalue denoted by hi. The population of ticks increases if lambda(1)<1 and decreases if lambda(1)>1. The lambda(1) 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 agr onomic measures decrease the encounter rate. This model permits to qua ntify the conditions of treatments (or of the efficacy of a vaccine) a nd of agronomic measures by which the populations are controlled. It s hows that the different treatment rhythms and the presence or not of t he wild or domestic refuges plays a major role on the dynamics of tick population. (C) 1998 Elsevier Science B.V.