Time evolution of non-lethal infectious diseases: a semi-continuous approach

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• Understanding the spread of infectious diseases is crucial for public health.
• Non-lethal diseases, like influenza, impact populations significantly.
• Mathematical models are essential tools for analyzing disease transmission.

Purpose of the Study:

• To propose a novel mathematical model for simulating the dynamics of non-lethal infectious diseases.
• To describe the time evolution of infectious individuals using a non-linear delay-differential equation.
• To assess the model's predictive capability using real-world disease data.

Main Methods:

• Development of a mathematical model based on a non-linear delay-differential equation.
• Population dynamics simulation with a focus on infectious individuals.
• Qualitative comparison of model predictions with epidemiological data.

Main Results:

• The proposed model effectively describes the dynamics of infectious disease spread.
• Model predictions show good qualitative agreement with influenza data.
• The model utilizes a limited set of parameters for its predictions.

Conclusions:

• The developed model provides a valuable framework for understanding non-lethal infectious disease dynamics.
• The model's accuracy with influenza data suggests its applicability to similar diseases.
• Further research can refine the model for more precise epidemiological forecasting.