Simulation of Isolation over time
Description
Purpose: The dataset simulates the progression of isolation over time, incorporating various aspects of isolation and potential intervention strategies. Components: Time: The dataset covers a simulated time period of 10 units, divided into 1000 equally spaced time points. Isolation Components: Withdrawal: Represented by a sine wave function, suggesting fluctuations in withdrawal tendencies. Rejection: Represented by a negative cosine wave function, indicating potential oscillations in feelings of rejection. Depression: Modelled by an exponentially decaying function, implying a gradual decrease in depression over time. Anxiety: Represented by a sine wave function with double the frequency, suggesting more rapid changes in anxiety levels. Interventions: Early Intervention: Aims to reduce the impact of withdrawal by halving its values when they exceed a threshold of 0.5. Coping Mechanisms: Represented by a placeholder function (to be replaced with a more accurate model), suggesting potential mitigation of depression symptoms. Model: The isolation_model function combines the values of each isolation component at a given time point to produce an overall isolation level. It also integrates the effects of interventions, modifying withdrawal and depression values based on their respective strategies. Visualisation: The code generates a plot of isolation levels over time, allowing for visual analysis of the simulated progression and the impact of interventions. Key Points: The dataset is simulated, not based on real-world measurements. The functions for isolation components and interventions are simplified representations. The primary focus is on exploring the interplay of isolation factors and potential intervention effects. Next Steps: Refine Intervention Models: Replace placeholder functions with more realistic representations of intervention strategies. Validate with Real-World Data: Compare simulated results with empirical data to assess model accuracy. Explore Additional Factors: Incorporate other relevant factors that contribute to isolation, such as social support or personality traits. Extend Timeframe: Simulate isolation over longer time periods to observe long-term trends and intervention outcomes.
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Steps to reproduce
import numpy as np import matplotlib.pyplot as plt # Constants total_time = 10 # Total time units time_points = np.linspace(0, total_time, 1000) # Functions representing different aspects of isolation def withdrawal(t): return np.sin(t) def rejection(t): return -0.5 * np.cos(t) def depression(t): return 0.8 * np.exp(-t) def anxiety(t): return 0.5 * np.sin(2*t) # Intervention strategies def early_intervention(component_values, threshold=0.5): return np.where(component_values > threshold, component_values * 0.5, component_values) def coping_mechanisms(component_values, threshold=0.5): return component_values + 0.2 * np.sin(2*np.pi*time_points) # Placeholder for coping mechanisms # Mathematical model for isolation def isolation_model(t): withdrawal_values = withdrawal(t) rejection_values = rejection(t) depression_values = depression(t) anxiety_values = anxiety(t) # Interventions withdrawal_values = early_intervention(withdrawal_values) depression_values = coping_mechanisms(depression_values) return withdrawal_values + rejection_values + depression_values + anxiety_values # Simulate and calculate isolation values over time isolation_values = isolation_model(time_points) # Visual representation plt.figure(figsize=(10, 6)) plt.plot(time_points, isolation_values, label='Isolation Model', color='blue') plt.title('Simulation of Isolation Over Time with Interventions') plt.xlabel('Time') plt.ylabel('Isolation Level') plt.legend() plt.grid(True) plt.show()