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Dynamics of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class
Mlyashimbi Helikumi1, Gideon Eustace1, Steady Mushayabasa2
1Mbeya University of Science and Technology, Department of Mathematics and Statistics, College of Science and Technical Education, P.O. Box 131, Mbeya, Tanzania.
Computational and Mathematical Methods in Medicine
|February 18, 2022
Summary
This study introduces a fractional-order chikungunya model with asymptomatic cases, revealing a disease threshold for persistence. Findings aid public health in predicting transmission and guiding control strategies.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Modeling
Background:
- Chikungunya virus (CHIKV) poses a significant public health threat, necessitating robust epidemiological models.
- Understanding disease dynamics, including the impact of asymptomatic individuals and memory effects, is crucial for effective control.
Purpose of the Study:
- To develop and analyze a nonlinear fractional-order chikungunya disease model incorporating asymptomatic infectious individuals.
- To investigate the influence of memory effects on chikungunya transmission dynamics.
- To estimate model parameters using real-world data and determine disease control thresholds.
Main Methods:
- A nonlinear fractional-order differential equation model was formulated.
- Qualitative analysis of model equilibria identified a disease threshold parameter.
- Model parameters were estimated using 2015 chikungunya case data from Colombia.
- The Adams-Bashforth-Moulton method was employed for numerical simulations.
Main Results:
- A critical threshold quantity was identified, determining chikungunya disease persistence or extinction.
- Asymptomatic individuals significantly impact both short-term and long-term disease dynamics.
- Threshold levels for preventative strategy efficacy were determined for disease management.
Conclusions:
- The proposed fractional-order model provides insights into chikungunya transmission, particularly the role of memory and asymptomatic cases.
- The findings offer valuable tools for public health authorities to predict disease spread and optimize control interventions.
- The study highlights the importance of considering memory effects and asymptomatic populations in infectious disease modeling.
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