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Published on: May 31, 2020
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A theoretical model for Zika virus transmission
Ebenezer Bonyah1,2, Muhammad Altaf Khan3, K O Okosun2
1Department of Mathematics and Statistics, Kumasi Technical University, Kumasi, Ghana.
Plos One
|October 5, 2017
Summary
This study presents a mathematical model for Zika virus (SEIR) transmission. Optimal control strategies including bednets, treatments, and insecticides were analyzed to curb disease spread effectively.
Area of Science:
- Epidemiology
- Mathematical Modeling
- Public Health
Background:
- Zika virus poses a significant public health threat, necessitating effective control strategies.
- Mathematical models are crucial for understanding disease dynamics and evaluating interventions.
Purpose of the Study:
- To develop and analyze a compartmental SEIR model for Zika virus transmission.
- To investigate the impact of constant and time-dependent control strategies on disease spread.
- To determine optimal control measures using Pontryagin's Maximum Principle.
Main Methods:
- Formulation of a Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model.
- Analysis of model stability for constant control scenarios.
- Application of Pontryagin's Maximum Principle for time-dependent optimal control.
- Numerical simulations to present and validate results.
Main Results:
- The steady states of the SEIR model with constant controls were found to be locally and globally asymptotically stable.
- Time-dependent controls, including bednets, treatments, and insecticide spraying, were optimized.
- Necessary conditions for effective disease control were derived using optimal control theory.
Conclusions:
- The SEIR model provides a framework for understanding Zika transmission dynamics.
- Optimal control strategies are essential for mitigating Zika epidemics.
- Mathematical modeling and control theory offer valuable tools for public health interventions.
