Joint force of individual, hospital, government: Simulation of the spread of 2019 novel coronavirus by multi-agents complex adaptive system

Early forecasting is important for health officials and decision-makers to respond to public health emergencies such as the 2019 novel coronavirus (COVID-19) outbreak. The spread of epidemic is mainly impacted by the interaction among agents, i.e., individual, hospital and government. In an effort to efficiently mitigate the impact of the virus, this original study designed a multi-agents complex adaptive system model of COVID-19 to detect the trend of the spread in 8 countries by simulating the adaptation and interaction among the agents. The results show that there should be 127,726 infections in China, 12,000 in South Korea, 729,377 in the USA, 176,623 in Italy, 194,359 in Spain, 165,122 in Germany, 177,462 in France and 149,540 in UK. It is impossible to screen and report all the cases, and the detection rate may be 82% in Italy, 65% in China, 55% in the USA, and 41% in UK on April 8, 2020. Scenario simulation results imply that action time is the most important factor in containing the spread of epidemic. If China had locked down Wuhan city five days later, the total infection would be tripled. The forces of individual, hospital and government should be united in fighting the virus.

3 Japanese citizens evacuated from Wuhan some scholars estimated that the ascertainment rate of infection was around 9.2% and incidence of infection in Wuhan can be 20,767 as of January 29, 20209. An exponential growth model was adopted to estimate the epidemic curve of COVID-19 cases in mainland China and found that there may be 469 unreported cases from 1 to January 15, 2020. The reporting rate after January 17, 2020 was likely to have increased 21-fold10. A simple diseasetransmission model of COVID-19 was established and found that reported number of cases remain lower than modeled estimates, but ascertainment is increasing over time11. A susceptible exposed infectious recovered metapopulation model was used to simulate the epidemics across China, and estimated that that 75,815 individuals have been infected in Wuhan as of January 25, 202012. Using the generalized logistic growth model, the Richards growth model, and the sub-epidemic wave model, Roosa et al. predicted that an average total cumulative case was between 37,415 and 38,028 in Hubei and 11,588-13,499 in other provinces by February 24, 202013.
These studies provide estimation results for COVID-19 in China. However, the forecasts made on different date vary widely. This is because the process of epidemic is full of dynamic and uncertainty, and traditional susceptible exposed infectious recovered model doesn't account for the adapting behavior of individuals, the changing of the medical resources and governments control power, or the interaction between them14. Complex adaptive system is a model to simulate the complex and changing reality15. It is an alternative approach to better reflect the adapting and changing nature of epidemic16. Many factors and multiple agents play different roles in the whole process which make it complex and adaptive17,18. Thus a multi-agents complex adaptive system model of epidemic is needed for the estimation19.
The aim of this study is to simulate the spread of COVID-19 using a multi-agents complex adaptive system model we originally designed, to reveal the roles of individual, hospital, and government in the prevention and control, to answer the questions about the time and number of peak infections, and to provide information for outbreak prevention and control policies in countries around the world.
The advantage of this model is simulating the reality of the process of epidemic incorporating two key features that are different from the previous studies: dynamic and adaptive. In our model, three agents which play the key roles are selected: individual, hospital, and government. The dynamic is reflected by the interaction and adaptation between agents, and parameters such as isolation rate and spread rate are adjusted with time. The adaptive is reflected by assigning values to parameters in a fixed interval, such as reproduction number, incubation period, recover or death period for each individual. In this study, 8 countries were selected as research objects: China, South Korea, the USA, Italy, Spain, Germany, France, and UK. The total infections, the peak of illness, and the detection rate

Detection rate
The multi-agents complex adaptive system model of COVID-19 is simulating the natural development of an epidemic, that is, how many individuals will be infected and when they will show symptoms. Due to the high proportion of individuals with mild symptom, a large number of illnesses will not be tested 6 and they cannot be included in the reported data. This study uses detection rate to measure the proportion of discovered illness. Detection rate is calculated by , where is actual data of accumulative confirmed cases and is simulated results of cumulative illness.
The detection rate inside Hubei, outside Hubei and total in the Mainland China are shown in Figure 4. In the early stage, due to insufficient detection capabilities, inadequate hospital admissions, and delays for patients to go to hospital, the actual reported data was smaller than (or lagging behind) simulated data. However, as the medical resource support assembled and the detection capability increased, there is still a gap between the simulated results and the real-time data. The detection rate may keep growing in the rest period of the epidemic. However, there are four factors making it difficult to reach a detection rate of 100%: (a) Asymptomatic self-recovery; (b) Symptomatic selfrecovery; (c) Patients who have symptoms but cannot be diagnosed due to nucleic acid test errors; (d) Patients who have progressed rapidly and died before their diagnosis. Due to the existence of these four situations, there will always be a gap between the true number of infection this study tries to simulate and the official reported number of confirmed cases.
The detection rates of all the studied countries on April 8, 2020 are shown in Figure 5. South Korea may have the highest detection rate of 85%, the detection rate of the USA is 55%, and UK may have the lowest detection rate of 41%.

Scenarios
The above results are simulated according to the real situation, for example, Wuhan city was locked down on January 23, 2020. What would happen if the lockdown be earlier or be later? This study designs three scenarios for China and South Korea and simulates the spread of the epidemic respectively (parameters are in Extended Data Table 5 and Table 7). The results are shown in Figure   6. Individual, hospital and government all play important roles in the prevention and control. In our model, the setting of parameters such as isolation rate and spread rate has a great influence on the simulation results. Medical resources of the hospital mainly affect isolation rate. Lockdown and restriction policy from the government and the obedience of the individual mainly affect spread rate.
Higher isolation rate, stricter policy and more cooperative individuals will reduce spread rate significantly.
This study provides a new approach of modeling COVID-19 by multi-agents influencing each other. If the government implements better prevention and control, the spread rate will decrease to a much lower level. 9 The reproduction number for every individual is 1 or 2 which means one infected person will spread the disease to 1 or 2 people in one day, but not every infected person go out and spread the disease.
How many infected people go out and spread the disease depends on the isolation rate and spread rate. The isolation period (ip) is an integer randomly assigned from 3 to 14. The recover or death period (rp) is an integer randomly assigned form 7 to 20. For every individual, once being infected at time t, he/she will be illed on day t+ip, and will be recover or die on day t+ip+rp. Once recovered or dead, the individual will be removed from the population.
The infection and illness are calculated in a matrix (please see Extended Data Figure 2). Taking the population size of n, isolation rate (ir) = 0, spread rate (sr) = 1 as an example, the calculation of the infection and illness is shown in Figure 3. The numbers in red represent the individuals from 1 to n. Who will be infected is chosen randomly, and the infected individual may be repeated because in the reality the close contacts may also be overlapping. This process is repeated from day 1 to day t. The number of rows with marks at day t is the number of cumulative infection CIt. The individuals will be illed on day Ti, Ti = t+ip, and will recover or die on day Tr, Tr = t+ip+rp. The parameter ip and rp are assigned separately for every individual. The number of illness on day t is the number of individuals whose Ti = t. The number of recover or death on day t is the number of individuals whose Tr = t.
The number of source St means how many infected individuals will spread the disease on day t. The Simulation results for the USA, Italy, Spain, Germany, France, and UK

Figure 4
Detection rate inside Hubei, Outside Hubei and in Mainland China Figure 5 Detection rates of the countries on April 8, 2020 18 Figure 6 Scenarios for China and South Korea

Supplementary Files
This is a list of supplementary files associated with this preprint. Click to download. Extendeddata.pdf