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Modelling epidemiological dynamics with pseudo-recovery via fractional-order derivative operator and optimal control
Samson Olaniyi1, Furaha M Chuma2, Ramoshweu S Lebelo3
1Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
Plos One
|January 30, 2025
Summary
This study introduces a fractional-order mathematical model to understand infectious disease spread with pseudo-recovery. Incorporating memory effects significantly reduces disease transmission through preventive and treatment strategies.
Area of Science:
- Epidemiology
- Mathematical Biology
- Dynamical Systems
Background:
- Infectious disease modeling often simplifies disease dynamics, potentially overlooking crucial factors like memory effects.
- Pseudo-recovery, where individuals appear recovered but can still transmit the disease, presents unique modeling challenges.
Purpose of the Study:
- To develop a novel fractional-order mathematical model for pseudo-recovery dynamics in infectious diseases.
- To investigate the impact of memory effects on disease transmission and control.
- To analyze the efficacy of time-dependent preventive and treatment strategies using optimal control theory.
Main Methods:
- Development of a deterministic mathematical model utilizing a fractional-order derivative operator (Caputo type).
- Qualitative analysis of model well-posedness using Banach fixed point theory.
- Sensitivity analysis of the basic reproduction number to understand parameter influence.
- Application of fractional optimal control theory and Pontryagin's maximum principle for strategy optimization.
Main Results:
- The fractional-order model successfully incorporates memory effects into pseudo-recovery dynamics.
- Sensitivity analysis revealed key parameters influencing disease spread.
- Optimal control simulations demonstrated that memory-dependent strategies significantly reduce disease transmission compared to memoryless approaches.
Conclusions:
- Fractional-order calculus provides a powerful framework for modeling memory effects in infectious diseases.
- Integrated preventive and treatment strategies, especially when accounting for memory, are highly effective in controlling disease spread.
- The study highlights the critical importance of considering memory in epidemiological models for accurate predictions and interventions.
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