Biomathematical Modelling and Stochastic Analysis

Modern biomathematics increasingly relies on mathematical models and theories to unravel patterns stemming from the intricate interactions occurring across various spatial, temporal, and hierarchical scales within biological systems. This necessity arises as a means to comprehend the complexities associated with the operation of biological systems and the spread of diseases. Diverse modeling approaches are employed to construct appropriate models. Examples of modeling approaches such as ordinary differential equation models, partial differential equation models, delay differential equation models, stochastic differential equation models, difference equation models, and non-autonomous models prove valuable. These approaches have the capability to offer practical strategies for the coexistence and conservation of endangered species, prevention of over-exploitation of natural resources, control of disease outbreaks, formulation of optimal dosing policies for drug administration, and more.

This thematic series focuses on biomathematical modeling and its associated analysis for interacting populations and significant epidemic diseases. We aim to provide a platform for the discussion of the major research challenges, appropriate methodologies, and recent achievements in the said directions. Appropriate mathematical models that offer fresh perspectives, meaningful model analyses, and validation through numerical simulations are highly appreciated. Potential topics include, but are not limited to:

• Nonlinear dynamic models of species interactions
• Nonlinear epidemic models and control of infectious diseases
• Spatio-temporal pattern formation in biomathematical models
• Stochastic biomathematical models
• Delay biomathematical models
• Non-autonomous biomathematical models
• Difference biomathematical models
• Numerical methods in biomathematical models and stochastic computing