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This R package implements an ODE-based model of the novel coronavirusoutbreak in Wuhan, China. It presents a simulator and likelihood functionassuming Poisson-distributed increments in the number of new cases in Wuhan,in the rest of China via the airline network, and to the rest of the world.

Data required:

• china_cases daily case reports in all Chinese cities (seedata(package='wuhan'))
• world_cases daily case reports from other countries (seedata(package='wuhan'))
• K daily numbers of passengers going between cities in China via airline network, available from OAG Traffic Analyzer
• W daily numbers of passengers going between Chinese cities and other countries via airline network, available from OAG Traffic Analyzer
• china_population the population size in each Chinese city (seedata(package='wuhan'))

Parameters:

• beta the human-human basic transmission rate
• gamma the removal rate (inverse of infectious period)
• I0W the number of initial infectives in Wuhan
• phi the case ascertainment rate in Wuhan

To use the package, assume the following workflow in R:

# Load required packages> install.packages('devtools')>devtools::install_git('https://github.com/chrism0dwk/wuhan.git')> library(wuhan)# Instantiate ODE model, simulate up to day 22.>simulator= NetworkODEModel(N=china_population,K=K,init_loc='Wuhan',alpha=1/4,max_t=22)# Instantiate LogLikelihood function>llik= LogLikelihood(y=china_cases[,1:22],z=world_cases[,1:22],N=N,K=K,W=W,sim_fun=simulator)# Find MLEs using optimisation>par_init= c(0.4,0.142857142857143,1,0.5)# Starting point>fit= optim(log(par_init),llik,control=list(fnscale=-1))>p_hat=fit$par

Asymptotic assumptions for confidence intervals fail in our case, since theparameter space is highly non-orthogonal. Confidence intervals are thereforecalculated using parametric bootstrap.p_hat is calculated on the log scale (logit scalefor thephi parameter), so needs to be transformed first:

>p_hat[1:3]= exp(p_hat[1:3])>p_hat[4]= invlogit(p_hat[4])

The samples can then be drawn by bootstrap, for which a computing cluster ishighly recommended (thanks Lancaster University HEC facility!).

>samples= bootstrap(p_hat,K,W,alpha=1/4,max_t=22,n_samples=1000)

Since the airline connectivity matrices are not included in this package, samplesfrom the parameters (for 4 different values of the latent period$1/\alpha$) areprovided as in-build datasets. Seedata(package='wuhan').