diff --git a/notebooks/ebola_model_test.ipynb b/notebooks/ebola_model_test.ipynb new file mode 100644 index 0000000..569f83d --- /dev/null +++ b/notebooks/ebola_model_test.ipynb @@ -0,0 +1,110 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "An example of using the Ebola model. Note that:\n", + "- We do not need to define a dummy state, tau, to denote time\n", + "- We should define the total population, N" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Illegal jump, x: [1.99985e+05 6.00000e+00 1.00000e+00 4.00000e+00 1.00000e+00 3.00000e+00], new x: [ 1.99984e+05 7.00000e+00 1.00000e+00 4.00000e+00 -1.00000e+00\n", + " 5.00000e+00]\n", + "Illegal jump, x: [1.99993e+05 3.00000e+00 0.00000e+00 0.00000e+00 1.00000e+00 3.00000e+00], new x: [ 1.99993e+05 3.00000e+00 0.00000e+00 0.00000e+00 -1.00000e+00\n", + " 5.00000e+00]\n", + "Illegal jump, x: [1.99684e+05 2.00000e+00 1.00000e+00 3.00000e+00 1.00000e+00 3.09000e+02], new x: [ 1.99684e+05 2.00000e+00 1.00000e+00 3.00000e+00 -2.00000e+00\n", + " 3.12000e+02]\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from pygom import common_models\n", + "\n", + "n_pop=200000 # population\n", + "i0=3 # initial infecteds\n", + "\n", + "# Initial conditions: [S, E, I, H, F, R]\n", + "x0 = [n_pop-i0, i0, 0, 0, 0, 0]\n", + "\n", + "# Timepoints\n", + "t = np.linspace(0, 30, 31)\n", + "\n", + "# Parameters from Legrand et al (https://doi.org/10.1017/S0950268806007217) for 1995 DRC outbreak\n", + "\n", + "ode = common_models.Legrand_Ebola_SEIHFR([('beta_I',0.588), # Transmission rate of infectious (weeks^{-1})\n", + " ('beta_H',0.794), # Transmission rate of hospitalised (weeks^{-1})\n", + " ('beta_F',7.653), # Transmission rate of dead during funeral (weeks^{-1})\n", + " ('omega_I',10.0/7.0), # Time between onset to recovery if not hospitalised (weeks)\n", + " ('omega_D',9.6/7.0), # Time between onset to death if not hospitalised (weeks)\n", + " ('omega_H',5.0/7.0), # Time between onset to hospitalisation (weeks)\n", + " ('omega_F',2.0/7.0), # Time between death and traditional burial (weeks)\n", + " ('alphaInv',7.0/7.0), # Incubation period (weeks)\n", + " ('delta',0.81), # Case-fatality ratio\n", + " ('theta',0.80), # Proportion of cases that are hospitalized\n", + " ('kappa', 0.1), # Timescale over which interventions come into effect (don't want this too quick) (weeks)\n", + " ('interventionTime', 8.0), # Time after simulation starts to begin interventions (weeks)\n", + " ('N', n_pop)]) # Population\n", + "\n", + "ode.initial_values = (x0, t[0])\n", + "# Set timestep to be 0.1 weeks since adaptive tau leap might struggle\n", + "ode.pre_tau=0.01\n", + "\n", + "# Simulate\n", + "np.random.seed(1)\n", + "n_sim=5\n", + "solution, jump, simT = ode.solve_stochast(t, n_sim, full_output=True)\n", + "\n", + "# Plot\n", + "f, ax = plt.subplots(1, 6, figsize=(15, 3))\n", + "for i_axis in range(6):\n", + " for i_sim in range(n_sim):\n", + " ax[i_axis].plot(t, solution[i_sim][:,i_axis], color=\"black\", alpha=0.5)\n", + "\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pygom", + "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": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/src/pygom/model/common_models.py b/src/pygom/model/common_models.py index 56cfecb..249d8d4 100644 --- a/src/pygom/model/common_models.py +++ b/src/pygom/model/common_models.py @@ -695,9 +695,8 @@ def Influenza_SLIARD(param=None): def Legrand_Ebola_SEIHFR(param=None): """ The Legrand Ebola model [Legrand2007]_ with 6 compartments that includes the - H = hospitalization and F = funeral state. Note that because this - is an non-autonomous system, there are in fact a total of 7 states - after conversion. The set of equations that describes the model are + H = hospitalization and F = funeral state. + The set of equations that describes the model are .. math:: \\frac{dS}{dt} &= -(\\beta_{I}SI + \\beta_{H}SH + \\beta_{F}SF) \\\\ @@ -711,27 +710,22 @@ def Legrand_Ebola_SEIHFR(param=None): -------- >>> import numpy as np >>> from pygom import common_models - >>> x0 = [1.0, 3.0/200000.0, 0.0, 0.0, 0.0, 0.0, 0.0] + >>> x0 = [200000-3, 3, 0.0, 0.0, 0.0, 0.0] >>> t = np.linspace(0, 25, 100) - >>> ode = common_models.Legrand_Ebola_SEIHFR([('beta_I',0.588),('beta_H',0.794),('beta_F',7.653),('omega_I',10.0/7.0),('omega_D',9.6/7.0),('omega_H',5.0/7.0),('omega_F',2.0/7.0),('alphaInv',7.0/7.0),('delta',0.81),('theta',0.80),('kappa',300.0),('interventionTime',7.0)]) + >>> ode = common_models.Legrand_Ebola_SEIHFR([('beta_I',0.588),('beta_H',0.794),('beta_F',7.653),('omega_I',10.0/7.0),('omega_D',9.6/7.0),('omega_H',5.0/7.0),('omega_F',2.0/7.0),('alphaInv',7.0/7.0),('delta',0.81),('theta',0.80),('kappa',300.0),('interventionTime',7.0),('N',200000)]) >>> ode.initial_values = (x0, t[0]) >>> solution = ode.integrate(t[1::]) >>> ode.plot() """ - # define our states - state = ['S', 'E', 'I', 'H', 'F', 'R', 'tau'] - # and initial parameters - params = ['beta_I', 'beta_H', 'beta_F', - 'omega_I', 'omega_D', 'omega_H', 'omega_F', - 'alphaInv', 'delta', 'theta', - 'kappa', 'interventionTime'] - - # we now construct a list of the derived parameters - # which has 2 item - # name - # equation - derived_param = [ + state_list = ['S', 'E', 'I', 'H', 'F', 'R'] + + param_list = ['beta_I', 'beta_H', 'beta_F', + 'omega_I', 'omega_D', 'omega_H', 'omega_F', + 'alphaInv', 'delta', 'theta', + 'kappa', 'interventionTime', 'N'] + + derived_param_list = [ ('gamma_I', '1/omega_I'), ('gamma_D', '1/omega_D'), ('gamma_H', '1/omega_H'), @@ -743,24 +737,14 @@ def Legrand_Ebola_SEIHFR(param=None): ('delta_2', 'delta*gamma_IH / (delta*gamma_IH + (1 - delta)*gamma_DH)'), ('theta_A', 'theta*(gamma_I*(1 - delta_1) + gamma_D*delta_1)'), ('theta_1', 'theta_A/(theta_A + (1 - theta)*gamma_H)'), - ('beta_H_Time', 'beta_H*(1 - (1/ (1 + exp(-kappa*(tau - interventionTime)))))'), - ('beta_F_Time', 'beta_F*(1 - (1/ (1 + exp(-kappa*(tau - interventionTime)))))') + ('t_trans', '(t - interventionTime)/kappa'), + ('beta_H_Time', 'beta_H*(1 - (0.5*(tanh(t_trans/2)+1)) )'), + ('beta_F_Time', 'beta_F*(1 - (0.5*(tanh(t_trans/2)+1)) )') ] - # alternatively, we can do it on the operate ode model - ode_obj = SimulateOde(state, params) - # add the derived parameter - ode_obj.derived_param_list = derived_param - - # define the set of transitions - # name of origin state - # name of target state - # equation - # type of equation, which is a transition between two state in this case - - transition = [ + transition_list = [ Transition(origin='S', destination='E', - equation='(beta_I*S*I + beta_H_Time*S*H + beta_F_Time*S*F)', + equation='(beta_I*S*I + beta_H_Time*S*H + beta_F_Time*S*F)/N', transition_type=TransitionType.T), Transition(origin='E', destination='I', equation='alpha*E', @@ -768,36 +752,34 @@ def Legrand_Ebola_SEIHFR(param=None): Transition(origin='I', destination='H', equation='gamma_H*theta_1*I', transition_type=TransitionType.T), - Transition(origin='I', destination='F', - equation='gamma_D*(1 - theta_1) * delta_1*I', + Transition(origin='H', destination='F', + equation='gamma_DH*delta_2*H', + transition_type=TransitionType.T), + Transition(origin='F', destination='R', + equation='gamma_F*F', transition_type=TransitionType.T), Transition(origin='I', destination='R', equation='gamma_I*(1 - theta_1)*(1 - delta_1)*I', transition_type=TransitionType.T), - Transition(origin='H', destination='F', - equation='gamma_DH*delta_2*H', + Transition(origin='I', destination='F', + equation='gamma_D*(1 - theta_1) * delta_1*I', transition_type=TransitionType.T), Transition(origin='H', destination='R', equation='gamma_IH*(1 - delta_2)*H', - transition_type=TransitionType.T), - Transition(origin='F', destination='R', - equation='gamma_F*F', transition_type=TransitionType.T) ] - bd_list = [Transition(origin='tau', equation='1', - transition_type=TransitionType.B)] + model = SimulateOde(state=state_list, + param=param_list, + derived_param=derived_param_list, + transition=transition_list) - # see how we can insert the transitions later, after initializing the ode object - # this is not the preferred choice though - ode_obj.transition_list = transition - ode_obj.birth_death_list = bd_list # set return, depending on whether we have input the parameters if param is None: - return ode_obj + return model else: - ode_obj.parameters = param - return ode_obj + model.parameters = param + return model def Lotka_Volterra(param=None): """