Mathematical modeling applied to epidemics: an overview

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Science

Background:

• Mathematical treatments have been crucial in epidemiology since the early 20th century, notably with the susceptible-infected-recovered (SIR) model.
• The evolution of epidemiological studies has seen increasing integration of advanced computational tools and statistical analyses.

Purpose of the Study:

• To provide an overview of the evolution of mathematical modeling in epidemiology.
• To explain the fundamental principles of the SIR model and its stochastic applications.
• To highlight the importance of computational tools like big data and complex networks in understanding disease outbreaks.

Main Methods:

• Review of the historical development of mathematical models in epidemiology.
• Presentation of the deterministic SIR model.
• Application of a stochastic approach to the SIR model within complex networks.

Main Results:

• Demonstration of the foundational role of the SIR model in epidemiological studies.
• Illustration of how stochastic approaches and complex networks enhance model realism.
• Emphasis on the essential contribution of computational tools and statistical analysis in contemporary disease outbreak analysis.

Conclusions:

• Mathematical modeling, enhanced by computational and statistical tools, is vital for understanding and managing epidemics.
• The integration of advanced methodologies is crucial for informing effective public health policies.
• The COVID-19 pandemic underscored the indispensable role of mathematical modeling in public health emergencies.