A simulation model for the physiological tick life cycle

Abstract

In this paper and following an approach used by two of the authors in (Nassif, N.R., Sheaib, D. (2009) On spectral methods for scalar aged-structured population models.) [5], we present a mathematical model for the tick life cycle based on the McKendrick Partial Differential Equation (PDE). Putting this model using a semi-variational formulation, we derive a Petrov–Galerkin approximation to the solution of the McKendrick PDE, using finite element semi-discretizations that lead to a system of ordinary differential equations in time which computations are carried out using an Euler semi-implicit scheme. The resulting simulations allow us to investigate and understand the dynamics of tick populations. Numerical results are presented illustrating in a realistic way the basic features of the computational model solutions.