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This volume convenes selected, peer-reviewed works presented at the Partial Differential Equations and Applications Colloquium in Honor of Prof. Hamidou Toure that was held at the University Ouaga 1, Ouagadougou, Burkina Faso, November 5-9, 2018. Topics covered in this volume include boundary value problems for difference equations, differential forms in global analysis, functional differential equations, and stability in the context of PDEs. Studies on SIR and SIRS epidemic models, of special interest to researchers in epidemiology, are also included. This volume is dedicated to Dr. Hamidou Toure, a Research Professor at the University of Ouaga 1. Dr. Toure has made important scientific contributions in many fields of mathematical sciences. Dr. Toure got his PhD (1994) from the University of Franche-Comte of Besancon, France, and is one of the key leaders and mentor of several generations of mathematicians in French-speaking Africa. This conference was purposely held in Ouagadougou in reverence of Dr. Toure's efforts for the development of mathematics in Africa since the beginning of his career in early 1982 to the current days.