isselkou-sedigh/SIRD-Modeling-COVID-19-Mauritania-2020-2022-

# SIRD Modeling – COVID-19 Mauritania (2020–2022) > Mathematical modeling of the COVID-19 epidemic in Mauritania using a SIRD model with time-varying transmission rates — analysis of 4 successive waves (2020–2022). --- ## Project Structure sird_mauritania/ │ ├── data/ │ └── covid19_mauritania_SIRD.xlsx # Epidemiological data (3 sheets) │ ├── scripts/ │ ├── create_data.py # Generate Excel data file │ ├── sird_simulation.py # SIRD model + simulation + figures │ ├── results/ │ ├── sird_simulation_results.csv # Numerical simulation results │ └── figures/ │ ├── fig1_sird_dynamics.png # S, I, R, D dynamics │ ├── fig2_model_vs_data.png # Model fit vs observed data │ ├── fig3_Rt.png # Effective reproduction number R(t) │ ├── fig4_dashboard.png # KPI dashboard │ ├── fig5_sensitivity.png # Sensitivity analysis (β) │ └── fig6_phase_portrait.png # S–I phase portrait │ └── README.md --- ## Mathematical Model ### Differential Equations The SIRD model is described by the following ODE system: $$\frac{dS}{dt} = -\frac{\beta(t) \cdot S \cdot I}{N}$$ $$\frac{dI}{dt} = \frac{\beta(t) \cdot S \cdot I}{N} - (\gamma + \delta) \cdot I$$ $$\frac{dR}{dt} = \gamma \cdot I$$ $$\frac{dD}{dt} = \delta \cdot I$$ with the constraint: $S + I + R + D = N = 4,736,139$ ### Parameters | Parameter | Symbol | Value | Description | |-----------|--------|-------|-------------| | Transmission rate (Wave 1) | β₁ | 0.285 day⁻¹ | Wild type strain | | Transmission rate (Wave 2) | β₂ | 0.312 day⁻¹ | Alpha variant | | Transmission rate (Wave 3) | β₃ | 0.387 day⁻¹ | Delta variant | | Transmission rate (Wave 4) | β₄ | 0.521 day⁻¹ | Omicron variant | | Recovery rate | γ | 0.0714 day⁻¹ | Infectious period ≈ 14 days | | Mortality rate | δ | 0.0056 day⁻¹ | Calibrated CFR ≈ 1.57% | ### Basic Reproduction Number $$R_0 = \frac{\beta}{\gamma + \delta}$$ ### Herd Immunity Threshold $$p_c = 1 - \frac{1}{R_0}$$ --- ## Installation ### Prerequisites - Python 3.9+ - pandas, numpy, matplotlib, scipy, open …