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Fractional epidemic model of coronavirus disease with vaccination and crowding effects
Suhail Saleem1, Muhammad Rafiq2,3, Nauman Ahmed4,3
1Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000, Pakistan.
Scientific Reports
|April 8, 2024
Summary
This study introduces a fractional order epidemic model for COVID-19, incorporating crowding and vaccination. The model demonstrates that control strategies effectively reduce infections and increase recovery rates.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Modeling
Background:
- The COVID-19 pandemic poses a global health crisis, with transmission significantly influenced by population density and vaccination efforts.
- Understanding the dynamics of coronavirus spread is crucial for developing effective control strategies.
Purpose of the Study:
- To propose and analyze a fractional order Susceptible-Infected-Vaccinated-Recovered (SIVR) epidemic model for COVID-19.
- To investigate the impact of crowding and vaccination on disease transmission dynamics.
- To ensure the mathematical validity and stability of the proposed fractional model.
Main Methods:
- Development of a fractional order SIVR model incorporating nonlinear incidence rates, crowding, and vaccination.
- Analytical determination of equilibrium points and application of fixed-point theory for existence and uniqueness.
- Stability analysis using Jacobian matrices, Routh-Hurwitz criterion, and Lyapunov functions.
- Calculation of the basic reproductive number using the next-generation matrix.
- Development and application of a non-standard finite difference (NSFD) scheme for numerical simulations.
Main Results:
- The model establishes conditions for the local and global asymptotic stability of disease-free and endemic equilibrium points.
- The basic reproductive number (R0) is calculated, with stability contingent on its value relative to 1.
- The NSFD scheme is proven to preserve the positivity and boundedness properties of the model solutions.
- Simulations demonstrate that control strategies reduce infected populations and increase recovered populations.
- The influence of the fractional order parameter on virus transmission is graphically analyzed.
Conclusions:
- The fractional order SIVR model provides valuable insights into COVID-19 transmission dynamics, highlighting the importance of crowding and vaccination.
- The proposed NSFD scheme offers a reliable numerical method for solving fractional epidemic models.
- Control strategies are effective in mitigating the spread of the virus and improving recovery rates.
- This research contributes to the understanding and prediction of future virus transmission trends.
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