PMC:7795931 / 23733-37525 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/7795931","sourcedb":"PMC","sourceid":"7795931","source_url":"https://www.ncbi.nlm.nih.gov/pmc/7795931","text":"3. Results and Discussion\n\n3.1. Modeling Framework\nOur model consists of two main systems: information dissemination system and behavioral response system. In the information dissemination system, each individual sends (receives) information to (from) its neighbors through an information network. Given that information will always be rapidly, extensively [22], and spontaneously [19] misrepresented during transmission, and that most people do not send more accurate information than they receive [17,18], we assume information gets distorted and misrepresented during each transmission. In the behavioral response system, each individual makes a move according to its information (with probability). Once informed about the epidemic, some people behave rationally such as practicing social distancing, while others behave irrationally such as flocking to churches [53], to supermarkets [54], and taking radical actions like repeated hospital visits [55].\nThe information dissemination system affects the behavioral response system. The government might intervene in the information dissemination to reduce infections by either disclosing or blocking information.\nFor information disclosing, the government discloses information to all individuals to make them behave rationally (or at least not behave irrationally). Obviously, the more accurate the information is and the earlier it is disclosed, the public can be better guided which lowers the final infection rate. However, it takes time for government to censor and screen information before disclosing, which brings an accuracy-speed trade-off. We use a disclosing threshold to measure the government’s preference on speed or accuracy; a higher threshold indicates a higher preference on accuracy: a threshold “1” means the government would not disclose any information unless it is completely accurate; while “0” indicates an immediate disclosure without any censoring and screening.\nFor information blocking, the government blocks less-accurate information transmissions between individuals. Obviously, a stringent blocking leads to a transmission of information with higher accuracy. However, blocking will slow down the overall information dissemination in the network, and then slow down the government’s censoring and screening of information. Thus, there is a trade-off between disclosing and blocking. We use a blocking threshold to measure the blocking stringency, the government would block any transmission of any under-threshold information: a threshold “0” means no blocking at all; while “1” means that government blocks all information transmissions.\nWe analyze both of the optimal thresholds for government. More details on the settings of our model can be found in the Methods section. In reality, the government has a great influence on the information dissemination. Thus, in our model, we assume that the government node is the most critical one and the government-disclosed information highly outweighs individuals’ information (except for the further discussion of a government with low credibility in a later section).\n\n3.2. Intervention Dilemma in Disclosing Information\nIn this part, we will discuss the speed-accuracy trade-off results and analyze the mechanism in information disclosing.\nFirst, Figure 3 summarizes the results of the simulations with 44 different external constraints, and we find that there is seldom a single dominant disclosing threshold (the government’s preference on speed or accuracy), i.e., seeking either speed or accuracy alone will not result in the lowest infection rate, and the optimal strategy (corresponding to the lowest infection rate at the end of the last period) is somewhere in between, which implies a speed-accuracy trade-off.\nSpecifically, the optimal disclosing threshold lies between both ends in about 84.09% of the cases, and their distributions vary in different external constraints. Figure 3a,b show that (1) if the initial information is 1 or 0.8 and the individual threshold is in [0,0.7], the optimal disclosing threshold has a 91.75% probability of being in the middle, and mostly (66.89%) falls within [0.6,0.8]; (2) if the initial information is 0.6 and the individual threshold is in [0,0.5], the government has a 93.00% probability of dealing with a trade-off (Figure 3c), and the optimal disclosing threshold mostly (77.78%) falls in [0.4,0.6]; (3) if the initial information is 0.4, the optimal disclosing threshold will almost certainly be greater than 0.4 (99.98%), but the distribution is too scattered to give a specific interval (Figure 3d). The mode of optimal disclosing threshold is 0.8 but only with 20.30% frequency.\nIn addition, we can see that, if the virus is medically well-known (ξ≥0.8) and public health awareness is low (XI≥0.7), the government shall prioritize accuracy over speed; if the virus is medically medium-known (ξ=0.6) and public awareness is high (XI≤0.5), the government shall balance speed and accuracy, which almost equally signifies; and if the virus in medically less-known (ξ=0.4), the government shall probably prioritize accuracy over speed.\nSecond, we will dissect the underlying logic and mechanism of the government’s trade-off. We take one of the curves in Figure 3a that is denoted by ξ=1 and XI=0.5, as an example, to find the relationship between disclosing the threshold infection rate, then we have Figure 4. In all 550 (11×50) experiments, the disclosing threshold for the lowest final infection rate usually lies between 0.7 and 0.9, and the final infection rate first falls then rises as the disclosing threshold increases, with the inflection point being at 0.8 (Figure 4a); the amount of final information per capita and the duration of government intervention both increase monotonically with the disclosing threshold (Figure 4b,e); the number of people infected after government intervention, the number of people infected by a panic after government intervention and the number of uninfected people remaining at the time of government intervention all negatively correlate with the disclosing threshold (Figure 4c,d,f).\nOne of the fundamental reasons for the government to balance speed and accuracy is the precipitous fall in the marginal contribution of accuracy as the disclosing threshold exceeds a certain “point”, while speed hardly affects the final infection rate. The following is a detailed analysis on the effects of both accuracy and speed.\nWith respect to accuracy, the effect comes from two perspectives: (1) accurate information lowers the infection from panic in a healthy panic-prone population (Figure 4d); (2) accurate information changes the behavior routine in the panic-prone population, which reduces the spread of the disease. Both (1) and (2) are in play until the disclosing threshold exceeds 0.5 (XI in our example); after that, there is no longer a panic-prone group, neither is infection from panic, which explains the precipitous fall in the marginal contribution of accuracy.\nWhen it comes to speed, the effect comes from two perspectives as well: (1) the time the government spends on censoring and screening information, which we call a lag; (2) the number of remaining uninfected people at the time of government disclosing information. The more accurate information the government seeks, the longer the lag (Figure 4e) and the fewer uninfected people remain at the time of disclosing (Figure 4f). Notice that both have roughly the same slope with respect to disclosing threshold, which explains a roughly constant marginal cost of pursuing accuracy.\nThe combination of constant marginal costs and abrupt fall in marginal benefits leads to an inflection point in disclosing threshold, which explains the heterogeneity in the distribution of optimal disclosing threshold: as disclosing threshold exceeds individual threshold, a sudden fall of benefits occurs, which theoretically makes the optimal disclosing threshold slightly greater than the individual threshold, which explains what we discussed above that the intervals in which the optimal disclosing threshold mostly lays differ.\nIn most cases, the government’s premature disclosing of inaccurate information will contaminate the overall network, while obsession with accuracy may have the government miss the disclosure window before too many people are infected, which is intolerable to government who requires a low infection rate. Thus, there is a trade-off.\n\n3.3. Intervention Dilemma in Blocking Information\nWe assume the government will block any transmission of under-the-blocking-threshold (XB) information between individuals; thus, XB=0 denotes the special case in previous discussion. Other settings are the same as above. In this part, we will discuss the optimal blocking strategies and analyze the mechanism.\nAs shown in Figure 5, the optimal blocking threshold varies from case to case. Overall, a small blocking threshold ([0.1,0.3]) is necessarily (100%) not optimal; a strict blocking threshold (XB≥0.8) is usually (50.41%) optimal, experimental data show a value between 45% and 55% in most external conditions; but 0 is the optimal threshold still in 20.25% of cases, and usually (89.80%) occurs when ξ≥0.8 and XI≤0.7. When the initial information is low (ξ≤0.6), not blocking is seldom (0.83%) optimal.\nWe have our key findings from the above analysis. First, minor blocking is not an option for government because it is dominated by stricter blocking in a deteriorated or being deteriorated information environment and undermines the efficiency of information dissemination in a benevolent environment. Second, in the age of the Internet, information is extremely interconnected and low-quality information is more easily disseminated, thus stricter information blocking might be an option worth considering in the early stages of an outbreak of an unknown infectious disease. Finally, if the virus is well-known at the medical level, plus the public has a certain level of health awareness, free spread of information might improve the situation; while, otherwise, as in the case of COVID-19, governments should intervene in the spread of information in social networks.\nFrom the simulation results, we can see that, in most cases, the optimal strategy will be either highly stringent blocking or free spread. Blocking low-quality information not only increases the overall information of the whole population, but causes side effects under certain external conditions. Thus, not blocking can be an optimal strategy in some cases. In this section, we provide an in-depth analysis of the data and a mechanistic analysis.\nFigure 5b reveals in general the optimal blocking threshold negatively correlates with initial information: as initial information drops from 1 to 0.4, the probability of optimal blocking threshold taking 0 will be 52.07%, 27.27%, 1.65%, and 0%, respectively. Figure 5c shows a positive correlation between optimal blocking threshold and individual threshold.\nGovernments block information mainly by suppressing less-accurate information, but which, once implemented, will slow down the overall information dissemination in the network anyway. Therefore, blocking can neither be too stringent nor too liberal, an optimal one usually lies in between. However, mild blocking is necessarily not optimal as it fails to purify the information environment.\nFurthermore, when the virus is well-known (ξ=1), especially when public health awareness is high (XI≤0.3), not blocking dominates most of the time (69.70%). While stringent blocking (XB≥0.8) is necessarily not (0%) an optimal strategy because higher-quality information, which helps to slow the spread of the disease with high public health awareness, is also blocked. Thus, when both the initial information and the level of public health awareness are at a high level, not blocking is optimal; otherwise, information that would not cause panic might do now. In addition, when medical awareness of the virus declines, so does the proportion of valuable information, which necessitates blocking as well.\n\n3.4. Optimal Intervention under Different Government Types\nIn previous sections, our study was based on the neutral government assumption that governments only seek the lowest infection rate. However, in reality, a government is not a personalized organization pursuing social optimum because it is often checked by various inside and outside nodes. In addition, government credibility makes a difference as well. In this section, we will discuss the optimal strategy for non-neutral governments and low-credible governments.\nAn unaccountable government that evades responsibilities would only care for lower new infections after intervention rather than global infections, which digresses from the objective described above. As shown in Figure 6a, the later the government discloses information, the less that will be newly infected after disclosure. There are two underlying reasons: (1) late disclosed information will indeed be more accurate, which reduces the infection rate; and (2) there are less uninfected people at the time of disclosing. Therefore, a blame-evading government would delay the disclosing to avoid being held accountable.\nA conservative government that prefers the least error-prone strategy (minimizing maximum loss) rather than the optimal one (the loss minimization strategy) would block all the information (Figure 6b). Since the optimal strategy would not be accessed until all external conditions are fully judged and scrutinized, which is not feasible for COVID-19, complete blocking would be optimal for such a government to avoid the worst case scenario. Our experiment of 484 different scenarios manifests a complete blocking will never lead to the highest 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