Mathematical and computational modeling of phenomena arising in population biology and nonlinear oscillations This book consists of a series of papers focusing on the mathematical and computational modeling and analysis of some real life phenomena in the natural and engineering sciences. The book emphasizes three main themes: (i) the design and analysis of robust and dynamically consistent nonstandard finite difference methods for discretizing continuous time dynamical systems arising in the natural and engineering sciences (ii) the mathematical study of nonlinear oscillations and (iii) the design and analysis of models for the spread and control of emerging and re emerging infectious diseases. Specifically some of the topics covered in the book include advances and challenges on the design analysis and implementation of nonstandard finite difference methods for approximating the solutions of continuous time dynamical systems the design and analysis of models for the spread and control of the COVID 19 pandemic modeling the effect of prescribed fire and temperature on the dynamics of tick borne disease and the design of a novel genetic epidemiology framework for malaria transmission dynamics and control. The book also covers the impact of environmental factors on diseases and microbial populations Monod kinetics in a chemostat setting structure and evolution of poroacoustic solitary waves mathematics of special (periodic) functions and the numerical discretization of a phase lagging equation with heat source.