International Journal of Technology and Applied Science

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Applications of Reaction-Diffusion Equations in Mathematical Biology and Population Dynamics

Author(s) Rajesh Kumar
Country India
Abstract Reaction-diffusion equations provide a powerful mathematical framework for studying biological systems in which local interactions occur simultaneously with spatial movement and dispersal. In this paper we provide a theoretical overview of the applications of reaction-diffusion models in mathematical biology and population dynamics, with particular emphasis on spatial diffusion in the evolution and distribution of biological populations. The reaction part represents local processes such as reproduction, mortality, competition, predation, and infection, whereas the diffusion part describes the movement of individuals or biological substances across a spatial domain. We discuss the applications of reaction-diffusion models in population growth, species competition, predator-prey interactions, biological invasion, and spatial epidemic dynamics. We focus on travelling-wave behaviour as a mathematical representation for population and disease spread in diverse environments. For long-term population behaviour, we study the role of spatial heterogeneity, diffusion rates, carrying capacity, and interspecific interactions. Besides classical models, in this work we briefly consider the new extensions of cross-diffusion, nonlocal dispersal, fractional operators, and heterogeneous environments. In summary, the reaction-diffusion equations provide a unified theoretical framework to explain how biological mechanisms are related to spatial population dynamics and to understand the emergence, persistence, and spatial spread of biological systems.
Keywords Reaction-diffusion equations; Mathematical biology; Population dynamics; Spatial diffusion; Species competition; Predator-prey models; Biological invasion; Travelling waves; Epidemic modelling; Spatial ecology; Population dispersal; Mathematical modelling
Field Physics > Nano Technology / Nuclear
Published In Volume 9, Issue 1, January 2018
Published On 2018-01-22
DOI https://doi.org/10.71097/IJTAS.v9.i1.1433
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Crossref DOI prefix of IJTAS is 10.71097/IJTAS

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