A Study Of Mathematical Models Towards Ecological And Epidemiological Process: Exploring the Interplay of Mathematical Models and Complex Ecological Systems

Abstract

As sub-fields of statistical biology, statistical ecology and epidemiology focus on the quantitativeanalysis of populations of organisms and their physical settings. Population biology, unsurprisingly, is aquantitative field of study. Population decline, growth, extinction, dispersal, immigration effects,emigration, population mixing, age-structure effects, etc. are all factors we will be interested in considering,clarifying, and forecasting as this discussion progresses. After years of intense collaboration betweenscientists working in different disciplines, the modern field of nonlinear science finally came into being afew decades ago. Different non-linear effects arise from mathematical biology's model equations (e.g.hysteresis, structural instability, dissipatory structures, dynamic disorder, etc.). Over the past twodecades, nonlinear dynamics has played a crucial role in the modeling of a wide range of biological andphysiological processes. Stability, periodicity, stochasticity bifurcation, fluctuations, and patternforming are just some of the characteristics of the system that have been studied and determinized,along with stochastic methods developed to address them, because of the critical importance of nonlineardynamic models of complex ecosystems and epidemiological systems. We have also looked at thetools and concepts of thermodynamics and statistical mechanics as they pertain to the investigation ofecologically complex systems.