# Importation, Local Transmission, and Model Selection in Estimating the Transmissibility of COVID-19: The Outbreak in Shaanxi Province of China as a Case Study

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## Abstract

**:**

**Background**: Since the emergence of the COVID-19 pandemic, many models have been applied to understand its epidemiological characteristics. However, the ways in which outbreak data were used in some models are problematic, for example, importation was mixed up with local transmission.

**Methods**: In this study, five models were proposed for the early Shaanxi outbreak in China. We demonstrated how to select a reasonable model and correctly use the outbreak data. Bayesian inference was used to obtain parameter estimates.

**Results**: Model comparison showed that the renewal equation model generates the best model fitting and the Susceptible-Exposed-Diseased-Asymptomatic-Recovered (SEDAR) model is the worst; the performance of the SEEDAR model, which divides the exposure into two stages and includes the pre-symptomatic transmission, and SEEDDAAR model, which further divides infectious classes into two equally, lies in between. The Richards growth model is invalidated by its continuously increasing prediction. By separating continuous importation from local transmission, the basic reproduction number of COVID-19 in Shaanxi province ranges from 0.45 to 0.61, well below the unit, implying that timely interventions greatly limited contact between people and effectively contained the spread of COVID-19 in Shaanxi.

**Conclusions**: The renewal equation model provides the best modelling; mixing continuous importation with local transmission significantly increases the estimate of transmissibility.

## 1. Introduction

_{0}), which is defined as the average number of secondary infections generated by an infectious person introduced into a completely susceptible population [5]. Although many methods of estimating R

_{0}have been developed [14,15], the difficulty in measuring R

_{0}of COVID-19 lies in the fact that it is a novel coronavirus. The knowledge of the well-known coronaviruses such as severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS) has been borrowed to understand the early transmission dynamics of COVID-19 [11]. Nevertheless, the epidemiological characteristics of COVID-19 appear quite different from those of both SARS and MERS [16]. Further, as R

_{0}is determined by the infectiousness of SARS-CoV-2 and the contact rate between individuals, its value should be different among regions that implemented different control measures. Therefore, the basic knowledge of COVID-19 epidemiological features should be obtained from the epidemic data during outbreaks.

_{0}, those studies used the daily number of cases, which implicitly summarised local and imported cases. During the early stages of the COVID-19 pandemic, one common feature among the outbreaks, except that in the epicentre, Wuhan city, was the continuous importation due to quick and easy modern transportation. During the outbreaks, the role played by imported cases is different from that of local cases when counting the transmissibility of SARS-CoV-2: local cases as a result of local transmission can increase R

_{0}, while imported cases as a potential source of transmission should reduce the estimate of R

_{0}. A previous modelling study of the spatial transmission of pandemic flu [25] shows that early importation plays a relatively more important role in estimating transmissibility. Models that mixed up continuous importation with local transmission enlarged the estimate of R

_{0}[18,19,20,21,22,23,24,26], and mislead our assessment. To get a reliable estimate of R

_{0}, it is crucial to separate imported cases from local cases [13,21,26,27,28,29].

_{0}during the early stage of the COVID-19 pandemic in mainland China and other similar situations and show how to select the best transmission model by comparing their fitting to outbreak data. Two models [17,24] have been used for analysing the Shaanxi outbreak. Bai et al. [17] proposed a Susceptible-Exposed-Diseased-Asymptomatic-Recovered (SEDAR) compartmental transmission model, and Yang et al. [24] used the Richards growth model. The same implicit and problematic assumption in their modelling is that the Shaanxi outbreak was caused by one importation event at the very beginning of the outbreak. Based on this assumption, they obtained nearly the same estimate of the basic reproduction number (2.95 and 3.11, respectively). In view of these two models, we will propose five models to analyze the Shaanxi outbreak: the Richards growth model, the renewal equation model, the SEDAR model, the SEEDAR model in which the exposure interval in SEDAR is divided into two with the latter one being infectious, and the SEEDDAAR model in which not only two exposed classes are present as in the SEEDAR model but there are two classes in both diseased and asymptomatic infections, so infectious periods following gamma-distributions. As we show below, the estimate of the basic reproduction number of COVID-19 during the Shaanxi outbreak under the actual continuous importation is below the critical level, 1.0, which is the consequence of the timely and draconian control measures implemented in Shaanxi province.

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Models

_{0}by calibrating the five models to Shaanxi outbreak data. The details of models and inference methods are given below.

#### 2.2.1. Richards Growth Model

_{0}seeds of infection at time t

_{0}, the Richards growth model states that the cumulative number of cases at time t is given by the following equation [24,33,39]:

_{0}= C(t

_{0}) seeds. If importation is continuing (e.g., there are C

_{i}cases that are imported at t

_{i}, i = 0,…, n − 1) and the outbreaks that importation at different times can cause are of the same final size K and growth rate r, then the total cumulative number of cases should be summarized as:

_{i}) is the Heaviside function: which is 1 if t > t

_{i}and 0 otherwise. The daily number of new local cases can be calculated as μ(t) = C(t) − C(t − 1). The basic reproductive number R

_{0}can be calculated from the growth rate and serial interval which is assumed to follow gamma-distribution g(τ;α,β) by [40,41]

#### 2.2.2. Renewal Equation Model

_{s}, dependent on time since infection of the case, s, but independent of calendar time, t. The distribution w

_{s}typically depends on individual biological factors such as pathogen shedding or symptom severity. For simplicity, the distribution w

_{s}is approximated by the distribution of serial interval (SI), the lag in onset dates of symptoms between an infector and its infectee. In the original renewal equation model, Fraser [42] considers a situation where the only importation is index case(s) at the very beginning of the outbreak and other cases are generated by local transmission (this assumption was also made in its direct application software for estimating the time-varying reproduction number [43]). During the spread of COVID-19 in 2020, the outbreak within a region (except the epicentre, Wuhan) took place with continuous importation. To take this into account, Fraser’s model is slightly modified as in the following (c.f., [44]). Let c

_{t}be the number of local cases whose symptoms onset at day t, its expected value is approximated by:

_{t}

_{−s}is the number of imported cases that have the onset date of symptoms on day t

_{−}s and w

_{s}represents the probability mass function of the SI of length s days, which can be obtained by ${w}_{s}=G\left(s\right)-G\left(s-1\right)$, with G(.) representing the cumulative distribution function of the gamma distribution. The gamma distribution is characterized by its mean SI_mean and standard deviation SI_sd, both of which are to be estimated jointly with R

_{0}from the outbreak data [45]. Because only 19 cases among 113 imported cases had symptom onset before entering Shaanxi province, the assumption that all cases started their infectivity duration within Shaanxi province, which is implicitly required in Equation (3), should be approximately satisfied.

_{0}) remained constant during the outbreak duration. This should be reasonable in view of the timely control measures implemented in Shaanxi province: control measures started on 21 January 2021 [36] and raised to their first-class emergency responses on 25 January 2020, just 2 days after the reporting of the first three imported cases in Shaanxi province [16,23]. To estimate the daily-varying transmissibility R

_{t}, Equation (3) is rearranged as:

_{t}can be estimated by the ratio of the number of new infections produced at time step t, c

_{t}, to the total infectiousness of infected individuals at time t, given by ${{\displaystyle \sum}}_{j=1}^{\mathrm{min}\left(t-1,SI\_max\right)}{w}_{s}({c}_{t-s}+{I}_{t-s})$, the sum of infection incidence, including both imported and locally generated, up to time step t−1 or the maximum of SI (whichever is the smallest), weighted by the infectivity function w

_{s}. R

_{t}is the average number of secondary cases that each infected individual would infect if the conditions remained as they were at time t [43], and it is used to monitor the change in transmissibility along the course of an outbreak.

#### 2.2.3. SEDAR Transmission Model

_{1}) progress to become diseased (I) and the other fraction (1 − θ) remains asymptomatic (A) but becomes infectious after an average latent period (L

_{2}). The diseased infections will be detected and admitted to hospital and isolated from the community after an average period of D

_{1}and the asymptomatic cases recover after an average infectious period of D

_{2}. The model can be described by the following set of differential equations:

#### 2.2.4. SEEDAR Transmission Model

_{3}, the duration of the late incubation period in which the infected person can pass the virus on, is introduced and is to be estimated (See Table 1).

_{0}for the SEEDAR model can be obtained by deriving the expression of the equilibrium number of susceptible people, and it is given by:

#### 2.2.5. SEEDDAAR Transmission Model

_{1}(t) and I

_{2}(t), and dividing asymptomatic compartment A(t) into A

_{1}(t) and A

_{2}(t). Adding the two new compartments to Equation (6), the model equations for the SEEDDAAR model are given as:

#### 2.3. Inference Method by Calibration to Shaanxi Outbreak

_{0}, SI_mean, SI_sd} for the renewal equation model, Θ = {β, L

_{1}, D

_{1}} for the SEDAR model and Θ = {β, L

_{1}, L

_{3}, D

_{1}} for the SEEDAR and SEEDDAAR models under the special situation where both asymptomatic and symptomatic infections are of the same latent period and infectious period (i.e., L

_{2}= L

_{1}and D

_{2}= D

_{1}). For simplicity, the proportion of symptomatic infections (θ) is set at 98.9% as reported [16]. Given the values of parameters Θ for the Richards growth model and the renewal equation model, simulating the time series of local infections, denoted as μ(t), t = t

_{start}, …, t

_{end}, is straightforward. Here, t

_{start}and t

_{end}represent the start day and end day of the outbreak data collected, respectively. For each set of parameter values of SEDAR, SEEDAR, and SEEDDAAR models, the Runge–Kutta fourth order method is used to solve the model equations and to obtain predicted time series of infections. In the inference of model parameters, directly observed cases of modified symptom onset dates (see the definition in the data above) are used as illustrated in the following. The likelihood function for the observed time series of local cases x(t), t = t

_{start}, …, t

_{end}, is given as:

#### MCMC Sampling

_{j}

^{(t−1)}, the new proposal is:

_{j}* = Θ

_{j}

^{(t−1)}+ σ

_{j}z.

_{j}is the step size of the j

^{th}parameter. The normal proposal density is given by:

_{j}* follows N(Θ

_{j}

^{(t−1)}, σ

_{j}

^{2}) (normal distribution with mean = Θ

_{j}

^{(t−1)}, and standard deviation = σ

_{j}). The proposal is accepted as the next step of the Markov chain with probability α = min(A,1), where:

_{j}*|y) the likelihood of parameter Θ

_{j}* given data y. For a truncated normal walk on the range (a,b), the proposal density is given by:

_{j}

^{(t)}= Θ

_{j}* if r < α (accepted);

Θ

_{j}

^{(t)}= Θ

_{j}

^{(t−1)}otherwise (rejected).

_{j}= 0.8σ

_{j}); if it exceeds 40%, then σ

_{j}= 1.2σ

_{j}. Otherwise, the jump step σ

_{j}remains unchanged. To allow the MCMC process to fully converge, a burn-in period of 400,000 iterations is chosen, and the estimates of model parameters are obtained from the further 400,000 iterations.

_{D}= mean(Dev(Θ)) − Dev(mean(Θ)) (i.e., posterior mean deviance minus deviance evaluated at the posterior mean of the parameters). The DIC is calculated as:

_{D}= mean(Dev(Θ)) + p

_{D}.

## 3. Results

#### 3.1. Estimates of SI and Incubation Period from Line List Data

#### 3.2. Estimate of R_{0} in Shaanxi Outbreak

#### 3.2.1. Richards Growth Model

_{0}being larger, less than, or equal to 1.0). Applying the Richards growth model to an infection spread process, it is implicitly assumed that its growth rate is positive and R

_{0}>1, which is wrong for the situation of well-controlled infections such as COVID-19 in Shaanxi province during January and February of 2020.

#### 3.2.2. Renewal Equation Model

_{0}) has a median of 0.61 and 95% CI from 0.54 to 0.68 (Table 1). The SI is estimated to have a mean of 4.66 days and an SD of 11.73 days, which is shorter than but comparable with the direct observation of SI from the outbreak (Figure 3). The model projection into next month (Figure 4B) indicates that the outbreak will die out within two weeks (i.e., the end of February 2020) and is unlikely to generate any further local cases under the current restriction measures.

_{t}shown in Figure 5 demonstrates how the transmissibility changed along the course of the outbreak. R

_{t}increased to about 2.0 within the first week, and then reduced to low values, but occasionally exceeding the critical value of 1.0. Its overall average is 0.61, which is equal to the median of posterior R

_{0}in the above model fitting. The change of R

_{t}reflects the stochasticity of transmission events within the Shaanxi outbreak.

#### 3.2.3. SEDAR Model

_{0}is estimated at 0.59 with 95% CI from 0.51 to 0.71 (Table 1). The incubation period is 1.8 days (95% CI: 1.6, 2.9), and the infectious period is 3.8 days (95% CI: 3.5, 5.3). The SEDAR model fitting and its prediction over one month ahead are shown in Figure 4C. Sensitivity analyses (data not shown) show that nearly the same estimates of model parameters are obtained when considering different values of latent period (L

_{2}) and infectious period (D

_{2}) for asymptomatic infections and the relative infectivity (ξ) of asymptomatic infections to symptomatic infections. This reflects the fact that, in the Shaanxi outbreak, the asymptomatic infections occupied a very small proportion of all infections (1.1%) [16] and therefore had small effects on model performance.

#### 3.2.4. SEEDAR Model

_{0}is estimated at 0.45 with 95% CI from 0.30 to 0.76 (Table 1). The incubation period of symptomatic infection is 5.0 days (95% CI: 1.3, 9.7), which is consistent with the observed values (mean = 6.76 days and sd = 4.41 days), and the infectious period of symptomatic infections is 4.8 days (95% CI: 1.6, 14.1), which is longer than the delay from the onset date of symptoms to hospitalization: mean = 3.71 days and sd=2.83 days (Figure 3). The duration of pre-symptomatic transmission (L

_{3}) is estimated at 1.5 days (95% CI: 1.0, 4.4 days); this suggests the fraction of transmission from strictly pre-symptomatic infections was about 1.5/(1.5 + 4.8) =24%, which is in agreement with previous estimates [46]. The SEEDAR model fits well with the observed data and predicts that the outbreak will die out within about three weeks (Figure 4D).

#### 3.2.5. SEEDDAAR Model

_{0}is estimated at 0.53 with 95% CI from 0.35 to 0.85 (Table 1). The incubation period of symptomatic infection is 5.3 days (95% CI: 1.3, 9.8), and the infectious period of symptomatic infection is 5.4 days (95% CI: 1.7, 14.0). The duration of pre-symptomatic transmission (L

_{3}) is estimated at 1.5 days (95% CI: 1.0 to 4.4 days). Those estimates of model parameters are very similar to those of the SEEDAR model. Similar to the SEEDAR model, the SEEDDAAR model equally well fits the observed data and predicts that the outbreak will die out within about three weeks (Figure 4E).

## 4. Discussion

_{0}of COVID-19 in the Shaanxi outbreak was well below the critical value of 1.0. This indicates that SARS-CoV-2 cannot self-sustain under the current control measures within Shaanxi province, China, and would stop once the importation of COVID-19 cases was halted. Our model successfully predicted the actual epidemic situation in Shaanxi province from late February 2020.

_{0}from the renewal equation and the SEDAR models are close to each other, and its estimates from the SEEDAR and SEEDDAAR models are lower; nevertheless, their 95% CIs are closely overlapped. Overall, the estimate of R

_{0}is in the range from 0.45 to 0.61. The model fittings to the local cases, shown in Figure 4, indicate that the renewal equation model provides the best fit to the observations and the SEDAR model is the worst. This is further confirmed by the values of DIC in Table 1 [55]: 127.9, 175.1, 160.5, and 160.8 for the renewal equation, and the SEDAR, SEEDAR, and SEEDDAAR models, respectively. Furthermore, the better performance of the SEEDAR and SEEDDAAR models than the SEDAR model confirms the existence of pre-symptomatic transmission [46]. It is worth mentioning that the SEEDDAAR model that has its infectious periods following gamma distribution does not appear better than SEEDAR that has its infectious period following simple exponential distribution. The Richards growth model, which is borrowed from ecological population dynamics [37,38], can provide a better model fit to the daily number of local cases than three compartmental transmission models (i.e., SEDAR, SEEDAR, and SEEDDAAR). However, the increasing trend of infections after the first month, which the Richards growth model predicts, deviates from the actual observation and hence invalidates the Richards growth model as an appropriate model for the Shaanxi outbreak.

_{0}[58]. In this study, we perform a joint estimation of R

_{0}and SI, and the results agree well with three compartmental models in estimation of R

_{0}and the empirical knowledge of SI [16,57]. Nevertheless, it should be kept in mind that the successful performance of the joint estimation of R

_{0}and SI in this study may be conditional on the very low proportion (i.e., 1.1%) of asymptomatic infections [58].

_{0}of about 3.0. Simple reasoning will show that this estimate is problematic. Let us consider a situation where all the 132 cases were generated within Shaanxi province only by the 113 imported cases, a rough estimate is R

_{0}= 132/113 ≈ 1.2. Some local cases might have been infected by other early local cases rather than directly from imported cases, which implies that the actual R

_{0}should be less than 1.2. With the similar treatments of continuous importation, the high and problematic estimates of R

_{0}for outbreaks in the major cities of China (except the epicentre, Wuhan city) were also reported [20,21]. Based on estimates of their SEDAR model parameters, Bai et al. [17] predicted that the Shaanxi outbreak would last until April 2020, which is more than one month longer than the actual occurrence. Our analyses show that the occurrence of the Shaanxi outbreak was mainly due to the large and continuous importation rather than the high local transmissibility of COVID-19 within the province. Furthermore, our prediction is consistent with what happened in Shaanxi province.

_{0}was estimated at 2.23 before 8th February 2020 and then it dropped to 0.04 [30]. Hao et al. [8] also confirmed the effectiveness of the timely prevention and control measures implemented in China in bringing the R

_{0}well below the critical level of 1.0. To check whether there was any potential breaking point in the transmissibility of COVID-19 within the Shaanxi outbreak, we calculated the instantaneous reproduction number R

_{t}[43]. The result shown in Figure 5 indicates that no clear pattern emerged that supported a potential breaking point in transmissibility although R

_{t}exceeded 1.0 on five days. In contrast, having mixed up imported cases with local cases, Yang et al. [24] used the renewal equation method [43] to obtain a time-varying reproduction number (R

_{t}), which persistently decreased over time and stayed beyond the critical level of 1.0 over more than half the course of the outbreak.

_{0}for the Shaanxi outbreak sharply differs from other studies which suggest R

_{0}= 2–7 [16,49,59,60] for SARS-CoV-2. In theory, R

_{0}is determined by the infectiousness of SARS-CoV-2 as well as the contact rate between people [5]. In the situation where no vaccine and effective drugs were available to protect people against the virus, the result of R

_{0}< 1 is due to the highly reduced contact rate between people [30]. This resulted from the timely and strong control measures implemented within Shaanxi province soon after it was announced in public on 20 January 2020 that COVID-19 could be transmitted among people. On the other hand, this indicates the success of the interventions executed in Shanxi province, China.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Timeline of the COVID-19 outbreak in Shaanxi province, China based on (

**A**) reported dates, (

**B**) dates of symptom onset, and (

**C**) modified dates of symptom onset. For modelling’s sake, the daily numbers of imported and local cases have been marked separately.

**Figure 2.**Flow chart of (

**A**) SEDAR transmission model, (

**B**) SEEDAR transmission model, and (

**C**) SEEDDAAR transmission model.

**Figure 3.**Distributions of (

**A**) serial interval (SI), (

**B**) incubation period, and (

**C**) delay from date of symptom onset to hospital visit. The blue pillars represent the data, and the estimate of the mean and its standard deviation in brackets are obtained by fitting gamma distribution to nonnegative data (red curve) and normal distribution to all data (black curves shown in the graphs).

**Figure 4.**Fitting of (

**A**) the Richards growth model, (

**B**) the renewal equation model, (

**C**) the SEDAR model, (

**D**) the SEEDAR model, and (

**E**) the SEEDDAAR model to outbreak data of symptom onset dates. Red dots represent the imported cases, and the blue triangles are the cases locally transmitted in Shaanxi province. The thick green line represents the median of MCMC samples, and the thin lines represent their upper and lower levels of 95% confidence intervals.

**Figure 5.**The effective reproductive number (R

_{t}) along the course of the outbreak in Shaanxi province, China under the SI distributions of SI_mean = 4.6 days, SI_sd = 11.7 days (the Maximum likelihood estimate of SI from model calibration of the renewal equation). R

_{t}is evaluated by averaging over one, two, and four days.

Parameter | Richards Growth | Renewal Equation | SEDAR | SEEDAR | SEEDDAAR | ||||
---|---|---|---|---|---|---|---|---|---|

Prior | Posterior | Prior | Posterior | Prior | Posterior | Prior | Posterior | Posterior | |

Growth rate (r) | [0,1.0] | 0.02 [0.012,0.032] | – | – | – | – | – | – | – |

Final epidemic size (K) | [1,6600] | 3315 [56,6521] | – | – | – | – | – | – | – |

Scaling exponent (ν) | [0.1,50] | 24.51 [0.72,48.81] | – | – | – | – | – | – | – |

Mean of SI (SI_mean) | – | – | U [3.5,10.0] | 4.66 [3.53,7.18] | – | – | – | – | – |

Standard deviation of SI (SI_sd) | – | – | U [3.0,15.0] | 11.73 [5.85,14.88] | – | – | – | – | – |

Transmission coefficient (β) | – | – | – | – | U [.001,0.5] | 0.155 [0.117,0.186] | U [.001,0.5] | 0.066 [0.029,0.154] | 0.072 [0.032,0.180] |

Latent period (L_{1}) * | – | – | – | – | U [1.6,14.0] | 1.81 [1.61,2.82] | U [1.0,10.0] | 5.04 [1.25,9.65] | 5.25 [1.28,9.76] |

Pre-symptomatic infectious period (L_{3}) | – | – | – | – | – | – | U [1.0,10.0] | 1.45 [1.04,4.43] | 1.45 [1.04,4.43] |

Infectious period (D_{1}) of diseased infections * | – | – | – | – | U [3.5,25.0] | 3.75 [3.51,5.16] | U [1.5,15.0] | 4.78 [1.61,14.06] | 5.40 [1.68,13.97] |

Dispersion parameter (η) | – | – | U [1.01,50.0] | 1.58 [1.06,2.86] | U [1.01,50.0] | 2.47 [1.56,4.431] | U [1.01,50.0] | 1.73 [1.08,3.26] | 1.71 [1.09,3.18] |

R_{0}^{♦} | – | 1.13 [1.08,1.21] | U [0.05,3.0] | 0.61 [0.54,0.68] | – | 0.59 [0.50,0.70] | – | 0.45 [0.30,0.76] | 0.53 [0.35,0.85] |

DIC ^{♣} | – | 140.2 | – | 127.9 | – | 175.1 | – | 160.5 | 160.8 |

_{2}= L

_{1}and D

_{2}= D

_{1}). As the proportion of asymptomatic infections is very small (i.e., 1 − θ = 1.1%), the other choices of these three parameters (say ξ = 1, L

_{2}= 2L

_{1}and D

_{2}= 2D

_{1}) do not noticeably change the estimates of the model parameters listed here. The priors for the SEEDAR and SEEDDAAR models are the same.

^{♦}: R

_{0}for the Richards growth model is calculated via equation (2) with the gamma-distributed serial interval of mean = 6.29 days and SD = 4.11 days (shape parameter = 2.343, rate parameter = 0.372).

^{♣}: Deviance information criterion (DIC) is a measure of model fitting.

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## Share and Cite

**MDPI and ACS Style**

Zhang, X.-S.; Xiong, H.; Chen, Z.; Liu, W.
Importation, Local Transmission, and Model Selection in Estimating the Transmissibility of COVID-19: The Outbreak in Shaanxi Province of China as a Case Study. *Trop. Med. Infect. Dis.* **2022**, *7*, 227.
https://doi.org/10.3390/tropicalmed7090227

**AMA Style**

Zhang X-S, Xiong H, Chen Z, Liu W.
Importation, Local Transmission, and Model Selection in Estimating the Transmissibility of COVID-19: The Outbreak in Shaanxi Province of China as a Case Study. *Tropical Medicine and Infectious Disease*. 2022; 7(9):227.
https://doi.org/10.3390/tropicalmed7090227

**Chicago/Turabian Style**

Zhang, Xu-Sheng, Huan Xiong, Zhengji Chen, and Wei Liu.
2022. "Importation, Local Transmission, and Model Selection in Estimating the Transmissibility of COVID-19: The Outbreak in Shaanxi Province of China as a Case Study" *Tropical Medicine and Infectious Disease* 7, no. 9: 227.
https://doi.org/10.3390/tropicalmed7090227