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Updated: Dec 11, 2025
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Vector Competence Analyses on Aedes aegypti Mosquitoes using Zika Virus
Published on: May 31, 2020
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Stability Analysis and Optimal Control for Yellow Fever Model with Vertical Transmission
1Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002 South Africa.
International Journal of Applied and Computational Mathematics
|August 25, 2020
Summary
This study models yellow fever (YF) transmission, finding fractional vaccine doses are insufficient for effective vaccination. Mathematical analysis and optimal control theory were used to assess control strategies.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- Yellow fever (YF) poses a significant public health threat, necessitating effective control strategies.
- Understanding YF transmission dynamics, including human-mosquito interactions and vertical transmission, is crucial for disease management.
Purpose of the Study:
- To develop and analyze a deterministic mathematical model for YF transmission dynamics.
- To evaluate the impact of control measures, including vaccination strategies, on YF spread.
- To determine optimal control strategies for YF prevention and management.
Main Methods:
- Construction and rigorous analysis of a deterministic mathematical model incorporating horizontal and vertical YF transmission.
- Analysis of mosquito-only dynamics to identify extinction equilibria.
- Computation of vaccinated and type reproduction numbers.
- Application of optimal control theory, Pontryagin's maximum principle, and modified forward-backward sweep technique.
- Numerical simulations and global sensitivity analysis.
Main Results:
- The mosquito-only model exhibits a globally-asymptotically stable mosquito-extinction equilibrium under certain conditions.
- Fractional dosing of yellow fever vaccine does not meet vaccination requirements.
- Optimal control strategies were characterized for disease management.
Conclusions:
- Fractional yellow fever vaccine dosing is inadequate for meeting vaccination requirements.
- Mathematical modeling and optimal control theory provide valuable tools for assessing and optimizing YF control strategies.
- Further research into effective vaccination schedules and integrated control measures is warranted.
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