Hawkes process modeling of COVID-19 with mobility leading indicators and spatial covariates

Overall Framework

Dependencies

Matlab 2018b

Functions

HawkPR.m: Main functions for EM algorithm.

Hawkes_Sim_Corona.m: Simulation of Hawkes processes after estimation.

updatep.m: Expectione step.

discrete_hawkes.m: discretize the simualtion results.

Quick run

Use MLE estimate shape and scale parameters for Weibull distribution

HawkPR('./input_data/NYT_Dconfirmed.csv', './input_data/GoogleMobi_Dconfirmed.csv', './input_data/Demo_Dconfirmed.csv', 14, '', '', 200, 7, 100, './output/mdl.mat', './output/pred.csv')

Specify shape and scale parameters for Weibull distribution

HawkPR('./input_data/NYT_Dconfirmed.csv', './input_data/GoogleMobi_Dconfirmed.csv', './input_data/Demo_Dconfirmed.csv', 14, 8, 4, 200, 7, 100, './output/mdl.mat', './output/pred.csv')

Function parameters

HawkPR( InputPath_report, InputPath_mobility, InputPath_demography, Delta, Alpha, Beta, EMitr, DaysPred, SimTimes, OutputPath_mdl, OutputPath_pred)

Functiona parameter	Description
InputPath_report	Input path for COVID daily report
InputPath_mobility	Input path for mobiblity report.
InputPath_demography	Input path for spatial demographic features.
Delta	Days lagged for mobility.
Alpha	Shape parameters for Weibull distribution. Leave it blank string as '' to allow MSE estimation.
Beta	Scale parameters for Weibull distribution. Leave it blank string as '' to allow MSE estimation.
EMitr	Maximum iterations for EM algorithm
DaysPred	Number of days to make prediction.
SimTimes	Simulation times for Hawkes processes. Nota that the prediction is the average of number of simulated events among all simulations.
OutputPath_mdl	Output path for the trained model.
OutputPath_pred	Output path for prediction results.

Input Data format

COVID daily report

• In csv file format. The header should contain "FIPS,State,County,x2020-02-15, ..."
• Date format is in x + 4 digits year + 2 digits month + 2 digits day, i,g., x2020-02-15.
• Each row is a covid daily report for each county.
• The total number of rows is the number of counties.

Mobility indices

• In csv file format. The header should contain "FIPS,State,County,Type,x2020-02-15 ..."
• Date format is in x + 4 digits year + 2 digits month + 2 digits day, i,g., x2020-02-15.
• Each row is a mobility indices for each county for each type of mobility.
• The total number of rows is the number of counties X number of mobility types

Spatial demographic features

• In csv file format. The header should contain "FIPS,State,County,Feature 1,Feature 2, ..."
• Each row is demographic features for each county.
• The total number of rows is the number of counties.

Examples of training data in './input_data/'

Functiona parameter	Description
NYT_Dconfirmed.csv	COVID daily confirmed cases collected by The New York Times (counties with confirmed cases >= 10)
NYT_Ddeath.csv	COVID daily deaths collected by The New York Times (counties with deaths >= 1)
GoogleMobi_Dconfirmed.csv	Google mobility of counties in NYT_Dconfirmed.csv (Imputated)
GoogleMobi_Ddeath.csv	Google mobility of counties in NYT_Ddeath.csv (Imputated)
Demo_Dconfirmed.csv	Demographic features of counties in NYT_Dconfirmed.csv
Demo_Ddeath.csv	Demographic features of counties in NYT_Ddeath.csv

Examples of output data in './output/'

mdl.mat

• model is save in mat files. (load('mdl.mat') can load the models in MATLAB)
• variable 'mdl' is the summary of Poisson regression model including coefficients
• variable 'mus' is the background rate (Exogenous infections)
• variable 'K0' is the estimated reproduction number
• variable 'alpha, beta' are the esimtated shape and scale parameter for the Weibull distribution

pred.csv

• In csv file format. The header should contain "FIPS,State,County,x2020_05_21 ..."
• Date format is in x + 4 digits year + 2 digits month + 2 digits day, i,g., x2020_05_21.
• Each row is a mobility indices for each county for each type of mobility.
• There are 'DaysPred' days of prediction starting from the day after the last day in COVID report.