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.
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Nassif, N., Sheaib, D., Jannoun, G.E. (2018). A Simulation Model for the Physiological Tick Life Cycle. In: Pinto, A., Zilberman, D. (eds) Modeling, Dynamics, Optimization and Bioeconomics III. DGS BIOECONOMY 2016 2015. Springer Proceedings in Mathematics & Statistics, vol 224. Springer, Cham. https://doi.org/10.1007/978-3-319-74086-7_13
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DOI: https://doi.org/10.1007/978-3-319-74086-7_13
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