{ "cells": [ { "cell_type": "markdown", "id": "5b20c072", "metadata": {}, "source": [ "# Parameter Inference for Time-Dependent SIRS Model\n", "\n", "We estimate parameters governing:\n", "\n", "- Infection rate $\\beta(t)$\n", "- Immunity waning $\\alpha(t)$\n", "\n", "from observed infection data $I_{\\text{obs}}(t)$.\n", "\n", "We consider:\n", "\n", "1. Deterministic inference (least squares)\n", "2. Bayesian inference (posterior distributions)\n", "\n", "---\n", "\n", "## Model\n", "\n", "$$\n", "\\begin{aligned}\n", "\\dot S &= -\\beta(t) S I + \\alpha(t) R \\\\\n", "\\dot I &= \\beta(t) S I - \\gamma I \\\\\n", "\\dot R &= \\gamma I - \\alpha(t) R\n", "\\end{aligned}\n", "$$\n", "\n", "---\n", "\n", "## Goal\n", "\n", "Estimate parameters:\n", "- $B_i$, $\\tau_i$, $\\sigma_i$\n", "- $\\rho_i$\n", "\n", "from data." ] }, { "cell_type": "code", "execution_count": 12, "id": "92449620", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import solve_ivp\n", "from scipy.optimize import least_squares" ] }, { "cell_type": "code", "execution_count": 13, "id": "a77d9af0", "metadata": {}, "outputs": [], "source": [ "gamma = 0.15\n", "iota = 3\n", "\n", "# initial guesses (to be estimated)\n", "B = np.array([0.3, 0.3, 0.3])\n", "tau = np.array([15, 60, 120])\n", "sigma = np.array([3.0, 3.0, 2.5])\n", "\n", "rho = np.array([0.05, 0.1, 0.1])\n", "\n", "rho_0 = 0.01\n", "B_0 = 0.05\n", "sk = np.array([0.25, 0.25, 0.15])\n", "T = np.array([30.5, 82.5, 144.5])" ] }, { "cell_type": "code", "execution_count": 14, "id": "fe277386", "metadata": {}, "outputs": [], "source": [ "def alpha(t, rho):\n", " result = 0\n", " for i in range(len(rho)):\n", " result += rho[i] * ((1 + np.tanh(t - (T[i] - iota/2)))/2) \\\n", " * ((1 - np.tanh(t - (T[i] + iota/2)))/2)\n", " return rho_0 + result\n", "\n", "\n", "def beta(t, B, tau, sigma):\n", " result = 0\n", " for i in range(len(B)):\n", " result += B[i] * np.exp(\n", " -0.5 * ((t - tau[i]) / (sigma[i] + sk[i]*(t - tau[i])))**2\n", " )\n", " return B_0 + result" ] }, { "cell_type": "code", "execution_count": 15, "id": "7f03bc46", "metadata": {}, "outputs": [], "source": [ "def solve_sirs(t_eval, params):\n", " B = params[:3]\n", " tau = params[3:6]\n", " sigma = params[6:9]\n", " rho = params[9:12]\n", "\n", " def model(t, y):\n", " S, I, R = y\n", " return [\n", " -beta(t, B, tau, sigma) * S * I + alpha(t, rho) * R,\n", " beta(t, B, tau, sigma) * S * I - gamma * I,\n", " gamma * I - alpha(t, rho) * R\n", " ]\n", "\n", " y0 = [0.99, 0.01, 0.0]\n", "\n", " sol = solve_ivp(model, (t_eval[0], t_eval[-1]), y0, t_eval=t_eval)\n", " return sol.y[1] # return I(t)" ] }, { "cell_type": "code", "execution_count": 16, "id": "ba16c400", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_data = np.linspace(0, 180, 100)\n", "\n", "true_params = np.concatenate([B, tau, sigma, rho])\n", "\n", "I_true = solve_sirs(t_data, true_params)\n", "\n", "# add noise\n", "noise = 0.002 * np.random.randn(len(t_data))\n", "I_obs = I_true + noise\n", "\n", "plt.plot(t_data, I_obs, 'o', label='Observed')\n", "plt.plot(t_data, I_true, label='True')\n", "plt.legend()\n", "plt.title(\"Synthetic data\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e8f4d684", "metadata": {}, "source": [ "## Least Squares Fitting" ] }, { "cell_type": "code", "execution_count": null, "id": "0c99b504", "metadata": {}, "outputs": [], "source": [ "# Reducing the parameter space\n", "tau_fixed = tau\n", "sigma_fixed = sigma\n", "rho_fixed = rho\n", "\n", "# Only estimate B\n", "initial_guess = B.copy()" ] }, { "cell_type": "markdown", "id": "a41e037f", "metadata": {}, "source": [ "Modifing Solver" ] }, { "cell_type": "code", "execution_count": 18, "id": "3816064b", "metadata": {}, "outputs": [], "source": [ "def solve_sirs_reduced(t_eval, B_params):\n", " def model(t, y):\n", " S, I, R = y\n", " return [\n", " -beta(t, B_params, tau_fixed, sigma_fixed) * S * I + alpha(t, rho_fixed) * R,\n", " beta(t, B_params, tau_fixed, sigma_fixed) * S * I - gamma * I,\n", " gamma * I - alpha(t, rho_fixed) * R\n", " ]\n", "\n", " y0 = [0.99, 0.01, 0.0]\n", "\n", " sol = solve_ivp(\n", " model,\n", " (t_eval[0], t_eval[-1]),\n", " y0,\n", " t_eval=t_eval,\n", " method='RK23', # faster\n", " rtol=1e-4,\n", " atol=1e-6\n", " )\n", " return sol.y[1]" ] }, { "cell_type": "code", "execution_count": 19, "id": "3572adb7", "metadata": {}, "outputs": [], "source": [ "def residuals(B_params):\n", " I_pred = solve_sirs_reduced(t_data, B_params)\n", " return I_pred - I_obs" ] }, { "cell_type": "code", "execution_count": 20, "id": "084742db", "metadata": {}, "outputs": [], "source": [ "lower_bounds = [0.0, 0.0, 0.0]\n", "upper_bounds = [1.0, 1.0, 1.0]" ] }, { "cell_type": "code", "execution_count": 28, "id": "0de8dd59", "metadata": {}, "outputs": [], "source": [ "result = least_squares(\n", " residuals,\n", " initial_guess,\n", " bounds=(lower_bounds, upper_bounds),\n", " method='trf',\n", " max_nfev=200\n", ")\n", "\n", "params_est = result.x" ] }, { "cell_type": "code", "execution_count": 30, "id": "88eb1c82", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.31771711 0.35998001 0.53712489]\n", "3\n" ] } ], "source": [ "print(params_est)\n", "print(len(params_est))" ] }, { "cell_type": "code", "execution_count": 31, "id": "cd368672", "metadata": {}, "outputs": [], "source": [ "I_fit = solve_sirs_reduced(t_data, params_est)" ] }, { "cell_type": "code", "execution_count": 32, "id": "7808ee4e", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 6))\n", "\n", "# Observed data\n", "plt.scatter(t_data, I_obs, s=25, alpha=0.7, label='Observed')\n", "\n", "# Fitted curve\n", "plt.plot(t_data, I_fit, linewidth=2, label='Fitted')\n", "\n", "# Residuals (scaled for visualization)\n", "residuals = I_obs - I_fit\n", "plt.plot(t_data, residuals, linestyle='--', label='Residuals')\n", "\n", "# Labels and formatting\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Infected proportion\")\n", "plt.title(\"SIRS Model Fit vs Observed Data\")\n", "\n", "plt.legend()\n", "plt.grid(True)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "eae37ef8", "metadata": {}, "source": [ "## Bayesian Inference (MCMC)" ] }, { "cell_type": "code", "execution_count": 33, "id": "77d0c6fb", "metadata": {}, "outputs": [], "source": [ "def log_likelihood(params):\n", " I_pred = solve_sirs(t_data, params)\n", " sigma_noise = 0.01\n", " return -0.5 * np.sum((I_obs - I_pred)**2 / sigma_noise**2)" ] }, { "cell_type": "code", "execution_count": 34, "id": "dc452352", "metadata": {}, "outputs": [], "source": [ "def log_prior(params):\n", " # simple box constraints\n", " if np.any(params < 0) or np.any(params > 2):\n", " return -np.inf\n", " return 0.0" ] }, { "cell_type": "code", "execution_count": 35, "id": "7bbeee8d", "metadata": {}, "outputs": [], "source": [ "def log_posterior(params):\n", " lp = log_prior(params)\n", " if not np.isfinite(lp):\n", " return -np.inf\n", " return lp + log_likelihood(params)" ] }, { "cell_type": "markdown", "id": "f8feb072", "metadata": {}, "source": [ "MCMC Sampler" ] }, { "cell_type": "code", "execution_count": null, "id": "8b483816", "metadata": {}, "outputs": [], "source": [ "def metropolis_hastings(init, n_samples=2000, step_size=0.01):\n", " samples = [init]\n", " current = init\n", " current_logp = log_posterior(current)\n", "\n", " for _ in range(n_samples):\n", " proposal = current + step_size * np.random.randn(len(init))\n", " proposal_logp = log_posterior(proposal)\n", "\n", " if np.log(np.random.rand()) < proposal_logp - current_logp:\n", " current = proposal\n", " current_logp = proposal_logp\n", "\n", " samples.append(current)\n", "\n", " return np.array(samples)" ] }, { "cell_type": "code", "execution_count": null, "id": "d50a3a18", "metadata": {}, "outputs": [], "source": [ "samples = metropolis_hastings(params_est, n_samples=3000)" ] }, { "cell_type": "markdown", "id": "1aa21258", "metadata": {}, "source": [ "Posterior visualization" ] }, { "cell_type": "code", "execution_count": null, "id": "858273e1", "metadata": {}, "outputs": [], "source": [ "plt.plot(samples[:, 0])\n", "plt.title(\"Trace of B[0]\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0e9af3fb", "metadata": {}, "source": [ "## Interpretation\n", "\n", "- Least squares provides point estimates.\n", "- Bayesian inference provides uncertainty quantification.\n", "- Posterior spread indicates identifiability of parameters.\n", "\n", "Key challenges:\n", "- Strong parameter correlations\n", "- Nonlinearity of the forward model\n", "- Identifiability issues in $\\beta(t)$ and $\\alpha(t)$" ] } ], "metadata": { "kernelspec": { "display_name": "venv", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.10" } }, "nbformat": 4, "nbformat_minor": 5 }