A predictive spatio-temporal model for bovine Babesiosis epidemic transmission.

The main purpose of this paper is to analyze a new dynamical model pertaining to bovine Babesiosis transmission, and investigate its consequent morphology. We present and study various ramifications of our mathematical model for bovine Babesiosis spread, given, firstly, by a temporal system of ordinary differential equations and, finally, by a spatio-temporal system consisting of reaction-diffusion equations. Diffusion terms are incorporated into the model, using specific derivations for both infected ticks and infected bovines. Furthermore, mechanisms for the nearest neighbors' infection are integrated into the model. We determine mathematically the basic reproduction number R0 via the next-generation matrix. Then, we analyze the stability of the equilibria and the effects of the mobility of infectious agents, being they either ticks or bovines. Finally, model-based analytical-numerical results are obtained and displayed in graphical profiles. The results of the proposed model and the health ramifications are then raised, discussed and validated.