We constructed a probabilistic model using reported mpox cases data and international air-travel data to estimate the according importation risk in Chinese mainland between April 14 and September 11, 2022. We also simulated effectiveness of two border screening strategies, and estimated the local outbreak probability considering different importation cases and parameters.

Simulating the international dissemination of the 2022–2023 multi-country mpox outbreak and evaluating Chinese mainland’s importation risk

To quantify the international importation risk of mpox from a source location \(i\) (regions with ongoing mpox transmission) to a destination location \(j\), we need to know the outbreak size in the source location \(i\) and the connectivity between the origin (location \(i\)) and destination (location \(j\)) by air-travel. We assumed that travel-associated mpox cases that contribute to the international spread mostly reside in major metropolitan areas with international airport transportation hubs. Hence, we considered a total of 39,114 mpox cases which occurred in 39 metropolitan areas with major international airports in the top 12 countries affected by mpox (Additional file 1: Tables S2 and S3) and evaluated their risk of exportations to Chinese mainland. Specifically, we obtained the time series of mpox incidence acquired outside Chinese mainland at the national level from Global.health [26]. We removed all travel-related cases from our analysis and assumed the rest of cases reside in the location of reporting and acquired infection in the location of reporting. We then decomposed the national-level time series into metropolitan-level proportional to the relative outbreak size of a metropolitan area with respect to its national total. For each mpox infection at the source location \(i\), we assumed that the infected individual could only make international air travel during the incubation period of \(\tau\) days (i.e., prior to symptom onset), which we drew from a lognormal distribution with an average of 8.94 days and standard deviation of 4.19 (Additional file 1: Table S4). For each case, we assumed there is a delay of \(\sigma\) days between symptom onset and the date of reporting, drawing from a zero-inflated negative binomial distribution with an average of 6.48 days and a standard deviation of 28.2 days (Additional file 1: Figure S1, Section S4). Consequently, if an mpox case is reported on date \(t\), this infected individual could potentially travel internationally between date \(t-\sigma\) and date \(t-\sigma -\tau\), i.e., during his/her incubation period.

We then estimated the international air-travel probability using the origin–destination air-travel data provided by OAG. The pandemic greatly influenced global air travel. We considered a pre-pandemic (upper-bound) scenario using the air-travel data of year 2019 and a peri-pandemic (lower-bound) scenario using the air-travel data of year 2022. For each air-travel scenario, if we denote the total air-travel volume at month \(m\) from location \(i\) to location \(j\) as \(_^\) (provided by OAG), the per-capita rate of international air travel \(_\) can be expressed as \(_=\frac_^}__}\), where \(_\) is the total population in location \(i\) and \(_\) is the number of days in month \(m\). We then iterated through all mpox cases and simulated each of their potential air-travel trajectory during their incubation period \(\tau\): starting from the beginning of the incubation period \(t-\sigma -\tau\), for each day forward \(t\) till the end of the incubation period \(t-\sigma\), whether the individual would travel on date \(t\) is simulated as a Bernoulli process with the probability of travel \(_\left(t\right)\) from location \(i\) is given by \(_=__\left(t\right)\). Given that the individual would travel on \(t\), then the destination \(j\) of the international travel would be decided based on a generalized Bernoulli distribution with the conditional probability of traveling to a specific location \(j\) given by \(\frac_\left(t\right)}__\left(t\right)}\) and the simulation for this infected individual ends. The simulation of the infected individual would also end if by the end of his/her incubation period \(t-\sigma\), the infected individual does not travel, and this individual would remain as a local mpox case in location \(i\). Once we iterate through all mpox infections globally, we could sum up the cumulative number of mpox importations from location \(i\) to location \(j\) up to time point \(t\), denoted as \(_\left(t\right)\). We repeated the entire simulation for a total of 200 times and obtained the distribution of \(_\left(t\right)\), denoted as \(P\left(_\left(t\right)\right)\) to capture the stochastic nature of the modelled process (Additional file 1: Figure S2). We could estimate the mean and 95% confidence interval (0.025 and 0.975 quantiles) of \(_\left(t\right)\) based on \(P\left(_\left(t\right)\right)\). To ensure the validity of our model, we performed a validation analysis of the mpox importations among countries where consecutive reports of mpox cases with international travel history were available, with abovementioned pre-pandemic and peri-pandemic air-travel volume setting the upper bound and lower bound of the importation risks, respectively (Additional file 1: Figure S3).

Quantifying the effectiveness of border screening against travel-associated mpox cases

To quantify the effectiveness of border screening policies, we first considered a scenario (denoted as Scenario 1 hereafter) that is in compliance with Chinese mainland’s current pandemic quarantine policy for border entry: according to the recently published (July 1, 2022) guidelines to mpox prevention and control by National Health Commission of the People’s Republic of China, all international travelers entering Chinese mainland, especially for those who had travel history to regions with an on-going mpox epidemic within 21 days of border entry, should be screened for mpox during their mandatory quarantine as a part of Chinese mainland’s pandemic response [27]. During the quarantine, individuals are also screened for mpox related symptoms including fever and rash. Symptomatic individuals with travel history from outbreak countries, close contact with confirmed cases, or contact with infected animals would be defined as suspected cases (Additional file 1: Table S5). Once detected, they would be reported to the local Centers for Disease Control and Prevention (CDC) and will be transferred to designated hospitals for a 21-day medical observation, and PCR test for lesion samples/swabs/blood will be conducted. Considering the variation of pandemic mandatory quarantine durations (ranging from 7 to 21 days) as well as the uncertainty on the proportion of people with mpox infections complying with self-reporting, we used a mathematical model to evaluate the proportion of imported mpox infections detected post entry screening (Additional file 1: Section S8). We also considered another hypothetical scenario (denoted as Scenario 2 hereafter) of plausible mpox entry screening in the absence of Chinese mainland’s pandemic quarantine policy for international travelers (a pre-pandemic scenario). In this scenario, international travelers with a self-reported mpox epidemiological link need to undergo medical observation for mpox-related symptoms (e.g., fever, rash, lymphadenopathy) during which they abstain from sexual activity, in addition to other precautionary measures [28]. Upon symptom onset, a suspected mpox case needs to self-isolate and seek testing. We also evaluated the effectiveness of this travel screening policy (Additional file 1: Section S8).

Estimating local outbreak probability

Following Hartfield et al.’s analytical solution of outbreak probability as a function of the basic reproduction number \(_\) and overdispersion parameter \(k\) [29] (Additional file 1: Section S9), we explored the range of mpox outbreak probability with one initial infector introduced into the high-risk population in Chinese mainland, with \(_\) ranging from 1.1 to 2.0 and dispersion parameter \(k\) ranging from 0.1 to 1.2 (Fig. 4a). Our best guess for \(_\) for the 2022 mpox outbreak is 1.8, according to a recent study conducted by Kwok et al. [30], and we considered a plausible dispersion parameter \(k\) of 0.88 through fitting the negative binomial distribution for the number of sexual partners among MSM in China [31, 32] (Additional file 1: Figure S4). For \(_\) = 1.8 and \(k\) = 0.88, we explored how the outbreak probability would change with the number of imported mpox cases missed by the border screening process (Fig. 4b). To understand the effect of emergency vaccination on preventing the outbreak probability, we used \(_\) to stand for the protection provided by emergency vaccination. The relationship can be illustrated as \(_=_\times S\), in which S stands for the proportion of population susceptible to mpox. We ignored the complexity of the different VE of one/two dose mpox vaccination in the US [33, 34]. We simply assumed 20% high risk population get effectively vaccinated, hence the \(_\) = 1.46.

Exploring the contribution of air travel and active MSM population size on outbreak in China

During June to November 2023, China has experienced a certain outbreak. We extracted monthly provincial reported number of mpox cases, and implemented a generalized linear model to testify the contribution of air-travel volume and active MSM population size at the province level estimated by Hu et al. [35]. We modeled with the permutation of these two metrics and the interaction.

All analysis was done in R (version 4.1.1; R Foundation for Statistical Computing, Vienna, Austria; https://www.r-project.org/).