Recent Studies based on Differential Equation Models and Nonstandard Finite Difference Methods for Infectious Disease Dynamics

Mathematical modeling developed a significant tool to understand spread and control infectious diseases. Numerous epidemic eruptions for example COVID-19, malaria, tuberculosis, hepatitis and Zika virus have exposed need for precise and dependable mathematical technique. Though, multiple usual numerical approaches fail to preserve positivity, stability and biological steadiness throughout simulations. Such studies summarize current growths within the field of differential equation models with nonstandard finite difference (NSFD) techniques which is mostly helpful in infectious disease dynamics.

Our study examines ordinary differential equation models, reaction-diffusion systems with dynamically reliable NSFD systems functional to dissimilar epidemic complications. Current findings helpful for NSFD techniques gives the better stability, preserve epidemiological properties and produce reliable numerical solutions associated with standard discretization methods. Our study also focusses role of vaccination, delay effects, diffusion, optimal control strategies in the epidemic modeling. Such methods have important applications like disease prediction, healthcare planning, epidemic prevention with public health decision-making.