Analysis of COVID-19’s Dynamic Behavior Using a Modified SIR Model Characterized by a Nonlinear Function
Abstract
:1. Introduction
2. Formulation of COVID-19 Mathematical Model
- 1.
- Symmetrical assumption: In this model, the capacity for virus transmission is identical for infected individuals, whether symptomatic or asymptomatic. Thus, groups (asymptomatic individuals) and (symptomatic individuals) are treated identically, following a common path to recovery with different transmission rates ( for asymptomatic individuals and for symptomatic individuals).
- 2.
- Asymmetrical assumption: The response to the virus varies among individuals; some develop symptoms, while others remain asymptomatic, creating an asymmetry in transmission. A certain percentage of the susceptible population develops symptoms (), while another percentage becomes asymptomatic ().
- 3.
- Natural mortality: Natural mortality affects all compartments of the model and represents a shared biological constant. Unlike the symmetrical and asymmetrical assumptions, this mortality does not distinguish between individuals based on their infectious status but reflects a universal biological reality.
3. Results
3.1. Principal Properties of the Model
3.1.1. Analysis of the Positivity of the Solutions
3.1.2. Invariant Domain
3.2. Asymptotic Stability Relating to the Disease-Free Equilibrium
3.2.1. Determination of the Basic Reproduction Number
3.2.2. Local Asymptotic Stability of the Disease-Free Equilibrium
- Since and according to the value of , we consider the following three scenarios: if , then and ; if , then and ; and if , then with both and where denotes the real part of a complex number. In summary, system (3) has a disease-free equilibrium () that is asymptotically stable if and only if is strictly less than 1. □
3.2.3. Global Asymptotic Stability of the Disease-Free Equilibrium
3.3. Asymptotic Stability of the Endemic Equilibrium
3.3.1. Local Asymptotic Stability of the Endemic Equilibrium
3.3.2. Global Asymptotic Stability of the Endemic Equilibrium
4. Sensitivity of the Basic Reproduction Number
5. Numerical Analysis
6. Discussion
7. Conclusion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description |
---|---|
b | Rate of population recruitment |
Rate of disease transmission from susceptible individuals (S) to infected compartments ( and ) | |
Constant of saturation reflecting psychological or inhibitory effects on the transmission of infection | |
Rate of susceptible individuals who develop symptoms of the disease | |
Rate of recovery from the asymptomatic population to the recovered population | |
Rate of recovery from the symptomatic population to the recovered population | |
Mortality rate attributed to COVID-19 | |
Rate of natural mortality |
Parameter | Value | Source |
---|---|---|
b | 0.05 | Assumed |
0.024 | Assumed | |
0.9 | Assumed | |
0.7 | [46] | |
0.25 | Assumed | |
0.14 | Assumed | |
0.023 | Assumed | |
0.01 | Assumed |
Parameter | Sensitivity Index |
---|---|
b | +1 |
+1 | |
−0.0116 | |
−0.0344 | |
+0.372 | |
−0.005 | |
−0.004 |
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Habott, F.; Ahmedou, A.; Mohamed, Y.; Sambe, M.A. Analysis of COVID-19’s Dynamic Behavior Using a Modified SIR Model Characterized by a Nonlinear Function. Symmetry 2024, 16, 1448. https://doi.org/10.3390/sym16111448
Habott F, Ahmedou A, Mohamed Y, Sambe MA. Analysis of COVID-19’s Dynamic Behavior Using a Modified SIR Model Characterized by a Nonlinear Function. Symmetry. 2024; 16(11):1448. https://doi.org/10.3390/sym16111448
Chicago/Turabian StyleHabott, Fatimetou, Aziza Ahmedou, Yahya Mohamed, and Mohamed Ahmed Sambe. 2024. "Analysis of COVID-19’s Dynamic Behavior Using a Modified SIR Model Characterized by a Nonlinear Function" Symmetry 16, no. 11: 1448. https://doi.org/10.3390/sym16111448
APA StyleHabott, F., Ahmedou, A., Mohamed, Y., & Sambe, M. A. (2024). Analysis of COVID-19’s Dynamic Behavior Using a Modified SIR Model Characterized by a Nonlinear Function. Symmetry, 16(11), 1448. https://doi.org/10.3390/sym16111448