Transportation, germs, culture: a dynamic graph model of 2019-nCoV spread

1School of Computer Science and Technology, Faculty of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, 710049 China. 2MOE Key Lab for Intelligent Networks & Networks Security, Faculty of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, 710049 China. 3School of Automation Science and Engineering, Faculty of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, 710049 China. 4Hugobiotech Co., Ltd., Beijing 100000, China. 5Genome Institute, the First Affili-ated Hospital of Xi’an Jiaotong University, Xi’an, 710061 China. 6The School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, 710049.China †To whom correspondence should be addressed. E-mail: kaiye@xjtu.edu.cn


Introduction
Since the outbreak of 2019 novel coronavirus (2019-nCoV) at the hardest-hit city of Wuhan, the fast-moving spread has killed over three hundred people and infected more than ten thousands in China 1 . There are more than one hundred cases outside of China, affecting a dozen of countries globally 2 . The genome sequence of 2019-nCoV has been reported and fast diagnostic kits, effective treatment as well as preventive vaccines are rapidly being developed 3 . Initial fast-growing confirmed cases triggered lock-down of Wuhan as well as nearby cities in Hubei Province. Mathematical models have been proposed by scientists around the world to project the numbers of infected cases in the coming days 4,5  factors. We hope that our model and simulation would provide more insights and perspective information to public health authorities around the globe for better informed prevention and containment solution.

Methods
In our model showed in Fig. 1A, we designed our dynamic graph model centered at transportation module as people take various transportation means to commute between places, considering that close-distance contacts during transportation are likely the most important factor aiding coronavirus transmission from infected to healthy ones. We built models accounting for taxi, bus, subway and walking with distinct capacities in the transportation module. We next placed stationary residential areas, public places and hospitals around the transportation module. Finally, we attached quarantine sites to hospitals. During each round of simulation, healthy or asymptomatic individual would start from one residential area, travel through the graph structure and returns to residence areas. Infected individuals would travel to hospitals after incubation period and remain at either hospital or quarantine sites if space allows. Otherwise, they will return to residential areas and seek medical care next day. The healthy individual becomes infected when he/she encounters infected ones during transportation or at any stationary areas. We performed the simulation beginning with one infected individual and observed the spread under various conditions.

Results
Although the major driver of pandemic spread are individuals with severe symptoms, data from Chinese cases in 2019-nCoV outbreak show signs of asymptomatic transmission.
Thus, we first investigated the effects of asymptomatic transmission on viral epidemic. We assume that the capability of spreading increases linearly during incubation period and reaches maximum strength when symptom appears. We set the length of incubation period as 7 days and compared with symptomatic transmission. It is alarming that it took asymptomatic transmission half number of days to infect 50% of the population as with symptomatic transmission took (Fig. 1B). Whereas symptomatic individuals are much easier to identify and isolate from the general public, asymptomatic individuals transmit viruses unconsciously, exacerbating the disease epidemic. We next simulated various scenarios with varying lengths of contagious asymptomatic periods and observed that longer contagious incubation period speed up the transmission significantly, perhaps due to longer period of unconscious virus spreading (Fig. 1C). Since the outbreak of 2019-nCoV, many cities have confirmed cases, mostly from Wuhan. We evaluated the effect of imported cases on the speed of spreading. As expected the more initial imported cases there are, the sooner 50% of the population are infected, as shown in Fig. 1D.
As transportation seems to be the major factor affecting the speed of spread, we simulated scenarios of typical cities around the world with different preferred transportation means.
For example, combined public transportation like buses, subways and taxis are often the daily commute means in China while driving is the primary choice in US. We also considered a hypothetic underdeveloped city, where public transportation limited. We found that Chinese cities with advanced public transportation are particularly vulnerable to virus spreading while limited public transportation in an underdeveloped city halts virus transmission (Fig. 1E) It is not unusual to require civilians to wear masks in public and to wash hands thoroughly in order to halt virus epidemic, but to lock-down major cities of the size like Wuhan requires considerate resources. We found that both personal protection (Fig. 1G) and city lock-down (Fig. 1H) halts transmission of virus immediately and the earlier installation of those orders the lower maximum number of infected cases. Although lockdown of the cities seems a radical administrative action, likely having a major impact on economy, the actions so far taken by Chinese authorities have certainly minimized the spreading of the virus globally.

Discussion and conclusion
Taken together, we conclude that actions taken by authorities in China such as locking down cities and strict requirement of personal protection and sanitization have reduced the viral spread significantly. Efficient and effective communication and well-educated general public are the keys to contain this pandemic spread. We recommend that CDC (center of disease control) or equivalent authorities in all countries shall pay close attention to possible asymptomatic transmission as dramatic changes in quarantine protocol are necessary if data supports its possibility.