On a two-strain epidemic mathematical model with vaccination.
Zakaria Yaagoub1, Jaouad Danane2, Karam Allali1
1Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, Mohammedia, Morocco.
Summary
This study models a two-strain epidemic with vaccination, finding that disease extinction occurs when the basic reproduction number is below one. High-strain reproduction numbers indicate dominance, impacting endemic stability.
Area of Science:
- Mathematical epidemiology
- Infectious disease modeling
- Public health dynamics
Background:
- Epidemic models are crucial for understanding disease spread.
- Non-monotonic incidence rates and vaccination strategies present complex dynamics.
- Analyzing multi-strain epidemics requires sophisticated mathematical frameworks.
Purpose of the Study:
- To mathematically investigate a two-strain epidemic model with non-monotonic incidence and vaccination.
- To analyze the stability of various equilibrium points.
- To determine the conditions for disease eradication and strain dominance.
Main Methods:
- Development of a seven-ordinary differential equation model.
- Analysis of four equilibrium points: disease-free, single-strain endemic, and co-infection endemic.
- Application of Lyapunov functions for global stability analysis.
- Calculation of the basic reproduction number (R0) for each strain.
Main Results:
- Disease eradication is achieved when the basic reproduction number (R0) is less than unity.
- Global stability of endemic equilibria is contingent on strain-specific R0 and inhibitory effects.
- The strain with a higher basic reproduction number tends to dominate.
- Numerical simulations support the theoretical findings on stability and dominance.
Conclusions:
- The model provides insights into the complex dynamics of two-strain epidemics under vaccination.
- The basic reproduction number is a key determinant of disease persistence and strain competition.
- Limitations exist in predicting long-term dynamics for certain R0 values.
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