key: cord-0903578-8f2jzaqz authors: Jing, Min; Ng, Kok Yew; Namee, Brian Mac; Biglarbeigi, Pardis; Brisk, Rob; Bond, Raymond; Finlay, Dewar; McLaughlin, James title: COVID-19 Modelling by Time-varying Transmission Rate Associated with Mobility Trend of Driving via Apple Maps date: 2021-09-02 journal: J Biomed Inform DOI: 10.1016/j.jbi.2021.103905 sha: c81ead0451eed379280ca3050ae20856b94874e0 doc_id: 903578 cord_uid: 8f2jzaqz Compartment-based infectious disease models that consider the transmission rate (or contact rate) as a constant during the course of an epidemic can be limiting regarding effective capture of the dynamics of infectious disease. This study proposed a novel approach based on a dynamic time-varying transmission rate with a control rate governing the speed of disease spread, which may be associated with the information related to infectious disease intervention. Integration of multiple sources of data with disease modelling has the potential to improve modelling performance. Taking the global mobility trend of vehicle driving available via Apple Maps as an example, this study explored different ways of processing the mobility trend data and investigated their relationship with the control rate. The proposed method was evaluated based on COVID-19 data from six European countries. The results suggest that the proposed model with dynamic transmission rate improved the performance of model fitting and forecasting during the early stage of the pandemic. Positive correlation has been found between the average daily change of mobility trend and control rate. The results encourage further development for incorporation of multiple resources into infectious disease modelling in the future. Mathematical modelling of infectious diseases plays an important role in understanding and controlling the transmission dynamics of epidemics such as coronavirus disease , which helps to identify the trends, make general forecasts and support the intervention measures. A well-established com- 5 partmental model is the SEIR model [1] , which divides the population into different compartments: Susceptible (S), Exposed (E), Infectious (I) and Recovered (R), then models how the disease transmits across the compartments over time. The SEIR model has been extended and widely applied to model the dynamics of COVID-19 [2, 3, 4, 5, 6, 7, 8, 9, 10] . 10 In the compartmental models, the parameters are often set based on individual decisions or assumptions, such as some infectious disease models may consider the transmission rate β remains as a constant during the entire epidemic. However, a constant β may not be adequate to capture the dynamics in reality because there are many external factors, such as intervention measures 15 or changes in social behaviours, that can influence the disease transmission. Therefore, a dynamic β is more desirable than a constant one. For example, a study [4] took social distancing into account and the authors proposed a timevarying β based on assumption that social behaviours would change due to the fear of increased deaths, then proposed a dynamic version of β modelled by daily 20 change of deaths. Although their assumption is limited since the transmission rates may change for many other reasons, not only a fear of increased deaths, their study provided a new idea for dynamic transmission rate for COVID-19 via integration of the epidemiological and economic models. They proposed a group-dependent contact rate, which measures the probability that a susceptible person in one group meets an infectious person from another group and 30 then they become infectious. They then took into account of social distancing in their model. Several studies have proposed a time-varying version of β [12, 13, 14] , which takes into account the subexponential growth dynamics in empirical data and the variety of mechanisms in the Ebola outbreak. A similar model was also extended to associate with the reproduction number R 0 [15] and 35 applied to study the 2014 Ebola Virus Disease (EVD) outbreak in West Africa [16] . Incorporating prior information into mathematical models or multimodal data fusion has been widely applied for healthcare applications such as for brain image decomposition [17] , fusion of EEG and fMRI [18] and prediction of clini- 40 cal measures from neuroimages [19] . However, integration of data from multiple sources in modelling of the infectious disease like COVID-19 has not been widely explored yet. Centers for Disease Control and Prevention (CDC) has published the factors contributing to COVID-19 acceleration [20] and many studies have been carried out in those areas. These factors include ongoing travel associ- 45 ated spread of the virus [7] [21] [22] , large gatherings [23] , introductions into highrisk workplaces/settings (such as hospital or care home) [24] [25], crowding and high population density[26] [27] , cryptic transmission (such as presymptomatic or asymptomatic spread [28] [29] ). Since these factors directly affect the infection occurrences, they may be potentially associated with infectious disease 50 modelling thereby improving modelling performance. However, it is not always easy to quantify such information to be used in modelling. Even if the information can be quantified, the way of incorporating it into the model may not be straightforward. Some studies have focused on using social contact matrices to quantify population contact patterns [30] or to associate the social contact 55 metrics with the reproduction number [31] . As for the research presented in this paper, the focus is to associate the mobility trend with the dynamic infectious disease models. 3 Recent studies for COVID- 19 have highlighted the importance of mobility trends in disease transmission. A study based in the USA [21] has revealed 60 that mobility patterns are strongly correlated with decreased COVID-19 case growth rates for the most affected 20 counties. They used daily mobility data derived from aggregated and anonymised mobile phone data to capture realtime trends in movement patterns for each US county, and used these data to generate a social distancing metric. Another study [7] worked on a SEIR-like 65 transmission model that included a network of 107 provinces in Italy connected by mobility at high resolution. This study did not use the mobility data in the model, but used it as a reference to assess the connection of the regions. A study [32] explored the relationship between the effective reproduction number and mobility levels during COVID-19 lockdowns for 56 countries based on the 70 mobility trend data obtained from Apple Maps [33] . Although these studies suggested the importance of mobility trend in disease transmission by analysing the relationship between their findings with mobility trend, they did not directly associate the mobility trend data in disease modelling. As a proof of concept, this study aimed to explore the potential of integrating 75 multiple data resource into infectious disease modelling thereby enhancing the model performance. In order to connect the disease model with the extrinsic factors that may contribute to disease transmission, a dynamic model with a control rate has been introduced, from which information from multiple sources can be incorporated within the model. In this study, the mobility trend data 80 was used as an example to associate with control rate, but other types of data (if can be quantified), such as a social contact matrix [34] may be used for different applications (involving social distancing or exiting strategies). The contribution of this study is based on three main aspects: 1) we modified with the disease intervention by incorporating the mobility trends (mobility of 90 driving via Apple Maps was used as an example). Different ways to process the mobility trend data were explored; 3) we investigated the relationship between the control rate and the processed mobility trend by predicting 20-day death rates in four stages. The results warrant further development for incorporation of mobility into infectious disease modelling. The rest of this paper is arranged as follows: in Section 2, the dynamic transmission rate is defined together with the simulation. The mobility trend data is introduced together with four ways of processing the trend data. In Section 3, the evaluation for model fitting and prediction based on six European countries are presented and results are discussed. The paper is finished with 100 discussion in Section 4 and conclusion in Section 5. Several studies based on 2014-2015 Ebola epidemic [12, 13, 14] have found the subexponential growth resulted in an early decline in effective reproduction 105 number due to rapid onset of behaviour changes and intervention strategies to control the spread of the disease. They proposed a time-varying version of transmission rate based on an "exponential decay" model to take into account the subexponential growth dynamics in empirical data. Similarly, restriction measures have been introduced to controlling the spread of COVID-19, which 110 have shown effective impact on control the acceleration of infection cases in most countries during the first wave of the pandemic. Some studies have observed the subexponential growth of COVID-19 in China [35] and in South Korea [36] due to effective containment and implementation of social distancing measures. To capture the subexponential growth dynamics of COVID-19, the timevarying version of β(t) based on an "exponential decay" model proposed in [12, 15] was adopted in this study, for example the transmission rate is exponentially declined from an initial value β 0 towards φβ 0 (for φ < 1) at a control rate Λ > 0. 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 Here, we modified their model and defined the dynamic β(t) as: where |·| denotes the absolute value. The transmission rate from an initial value 115 β c changes to β 1 under the control rate Λ, which governs the speed of the disease spreading over time. When there is no control, Λ = 0, the transmission rate is a constant β c (as in conventional SEIR model). Here we considered the possible change in both directions, especially after relaxing the level of restrictions such as easing lockdown, therefore the absolute change of |β c − β 1 | was used. The impact of control rate on the dynamic model is demonstrated by plotting β(t) in Fig. 1 (a) (with β c = 1.0 and β 1 = 0.2β c for demonstration purpose). As seen in Fig. 1 (a) , the higher the control rate the quicker β(t) declines. Fig. 1 β(t) was applied to a modified SIR model [4] , such as where S = susceptible, I = infectious, R s denotes resolving, i.e. sick but not infectious, D is deceased, C is recovered, and N is the population. Infectiousness capacity. Fig. 2(b) shows the fluctuations of infected cases under β(t) with noise, but overall the similar impact of control rate can be observed as in Fig. 2 (a). β(t) with noise. It can be seen that in the dynamic model, a higher control rate not only delays but also lowers the peak of infected cases. In the experiments for real data, we applied β(t) to the general SEIR (GSEIR) model proposed in [3] , which was based on study for COVID-19 in China and has also been applied to COVID-19 study in Spain [40] [41] and Italy [42] . Apart from S, E, I and R in the classical SEIR model [1] , GSEIR model introduced three additional states to model the epidemic dynamics, which are Quarantined 155 Q, Deceased D and Insusceptible P . The quarantine state Q was originally proposed in [43] , which was used to refer the isolated individuals (as in quarantine). In GSEIR model, the period from I to Q was defined as the time from the infectious to the case being confirmed. The block diagram of the GSEIR model with dynamic β(t) is shown in Fig. 3 and the dynamic GSEIR model can 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 be expressed by a set of ordinary differential equations (ODEs) as in Eq. (3). The total population N = S + E + I + Q + R + D + P . A set of coefficients The LSE optimisation usually can provide a good fit to the data, however, some auto-fitted parameters may not be plausible from the perspective of infec- 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 tious disease, especially for those associated with γ −1 , latent period, and δ −1 , the period between infectious (I) to becoming confirmed Q. (For example, for the data from UK, the auto-fitted parameters for latent period γ −1 = 0.5 day and δ −1 = 33 days, which appear far from the reality and those reported in the literature). In GSEIR model, the period from I to Q was defined as the 175 time from the infectious to the case being confirmed, which can vary for different countries depending on the disease control policy. Therefore, we fixed the The latent period, γ −1 , is the period between the time at which a person is 185 exposed to the virus (E) to the time which they become infectious (I). During this period, the pathogen is present in a "latent" stage, without clinical symptoms or signs of infection in the host. Currently, there is no agreement on how long it takes an infected individual to become infectious. It has been reported [9] and is largely accepted, that transmission of COVID19 infection may occur 190 from an infectious but asymptomatic individual. In [44] , it was reported that the median time prior to symptom onset is 3 days, the shortest time is 1 day and the longest period as much as 24 days. Another study [7] summarised that the latency period reported in the literature varies from 3.44 -3.69 days [5] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 symptoms are asked to self-quarantine for at least 7 days (for individual) or 14 days (for the whole household) before going to hospital for a test. Therefore, it is not easy to use one value for all countries, final value of δ −1 was set within a range between 5 -14 days. It is noticed that the cure rate and recovery rate are also defined as timevarying, which can be decided in different ways. In [3] they were based on estimation from the reported recovered and mortality data in China. Here we adopted the simple functions being used in [47] [40] [41] , in which the cure rate increases and mortality rate decreases over time, such that: For each country, the parameters λ 1 , λ 2 , k 1 and k 2 were added to the set of coefficients θ to be estimated by model fitting, so they can be different for each country. For those who are interested in tailoring the parameters of cure rate and recovery rate to suit individual country scenarios, more variations of functions and implementation can be found in [47] . 215 Theoretically, the control rate can be associated with different types of disease control measures as long as they can be quantified, which however is not always easy in practice. In this study, we used the mobility trend as an example 220 and explored how they can be associated with the infectious disease models. The daily global COVID-19 mobility trend data published by Apple Maps [33] were used in the study. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 In Fig. 4 To incorporate the mobility trend data to the dynamic model, one instinctive 260 idea was to directly apply the mobility trend as the control rate in Eq.(1). However, more consideration was needed before that. For example, the mobility trend data needs to be processed before linking to the disease models. There were different ways to process the trend data, which one should be used? or based on what criterion? In terms of technical implementation, one may also 265 need to consider whether the mobility trend should be incorporated using a fixed value or as a time series (which is more challenging technically). In the present study, the focus was to find out which format of processed mobility trend can be associated with the control rate via measuring the correlation (as shown in the later experiments). Further development of direct incorporation of mobility 270 trend in the dynamic model will be considered in the second phase of the study. Next, we introduce four types of processing for the mobility trend, which can be applied to countries individually. For each country, the control rate Λ was considered to be proportional to the mobility trend M t , such as Λ ∝ M t . The trend M t can be expressed in two different forms, the 7-day smoothed daily mobility trend M d (t) (> 0) and the daily change of mobility M c (t) comparing to baseline M b , which can be presented as: 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 and It is noticed that the mobility trend M d (t) is always positive but daily change and two types of average of M c (t) can be calculated by: 7 ). In the experiments, we investigated how the control rate can be associated 275 with the mobility trend in these four different forms. Evaluation of model performance can be carried out by different ways, such as via model fitting or prediction. Model fitting is to fit a model to experimental 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 The COVID-19 data for UK, Italy, Spain, France and Germany were obtained from Johns Hopkins University data repository [8] , and the data for NI were obtained from COVID-19 UK Data via Github [48] . For each country, the data includes the case numbers for the total confirmed cases, deaths and recovered cases each day, which are required for infectious disease modelling. It 295 has been noticed that the data for the recovered cases in the UK and NI were not properly reported. For Spain and France there were some data fluctuations in some days, such as reduced numbers in cumulative cases, which could be due to the issues in these countries' reporting system. The instability of data may affect the performance in the results. The mobility trend data is available via 300 Apple Maps [33] and has been explained in Section 2.3.1. The parameters for γ −1 , δ −1 , E(0) and I(0) used in the experiments and the starting date for the data in each country are summarised in Table 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 The proposed model was fit to the 100 day data and the performance was The comparison of performance by RMSE and MAE for SEIR, GSEIR and the proposed method is given in Table 2 for deaths and Table 3 for the confirmed cases, respectively. The best result for each measure for a given country is in bold. It can be seen that the proposed method outperformed SEIR and GSEIR for both fitting for deaths and confirmed. The optimal control rates for deaths 320 and confirmed are slightly different for some countries, which can be due to the complexity of the reported data. For example, the number of confirmed cases can be affected by testing capability, reporting system and disease control policy. Like some studies [4] that focused on the mortality data only, the following experiments for prediction just used the mortality data. The results of model fitting by the proposed method are given in Fig. 5 for the cumulative confirmed cases and deaths. Fig. 6 presents the results for the daily confirmed cases. There are several noticeable spikes and drops in the daily data for France and Spain, which may be due to possible adjustment made by these countries in their data reporting system. For example, as seen in Fig. 330 5 for Spain, the reported cumulative confirmed cases dropped during 50 to 60 days, which explains the negative number of daily confirmed cases in Spain in 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 It is also noticed that the model may not perfectly represent the saddle 335 point of infection in the UK between time (days) 30 and 60 (as seen in Fig. 6 ), which may be due to the data for the recovered cases in the UK was not properly reported. Technically, a better fitting performance can be achieved by adjusting the parameters via auto-fitting by LSE optimisation, however, as explained in Section 2.2.2, those parameters may not be explainable from the perspective 340 of infectious disease. In the experiment, we applied the proposed method to the data from six countries. The purpose was not to compare the performance among those countries but to evaluate the performance of the proposed method. The overall performance shows that the model fits well with the data. The results suggest a relatively consistent performance was achieved from different 345 countries, which is encouraging for future studies. 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 To investigate how the control rate can be related to the mobility trend, we processed the mobility data in four different ways as explained in Section 2.3.2. The average of mobility was calculated per 20 days and per +20 days, which 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 For example, Fig. 7(a) per +20 days M c2 in Fig. 7(b) presents slightly different trends to those in Fig. 7 (a). The average mobility M d1 in Fig. 7 (c) and M d2 in Fig. 7 (d) present the same trends as in Fig. 7(a) and Fig. 7(b) , respectively, however in different scales (as shown in y-axis). The evaluation of the performance for prediction was carried out based on the prediction of deaths at four stages, in which four data lengths were used (as those set for mobility processing). In practice, it is better to use as much data available as possible to fit the model before forecasting the unseen case numbers in future days. To ensure the prediction was completely out-of-sample, in the 370 first stage prediction, data from the first 1-20 days were used to estimate the parameters, which then were used to predict the deaths cases for the next 20 days (shown in the column of Days for Prediction as 21-40 in Table 4 and Table 5 ). At the second stage with more data available, the data from 1-40 days were used for model fitting then the parameters were applied to predict for days 60, and so on so forth. The RMSE and MAE were calculated at each stage between the predicted 20 days and their corresponding reported data only. The comparison of RMSE and MAE for prediction by SEIR, GSEIR and the proposed model are given in Table 4 , and the results of corresponding control rate and mobility trend processed in four different ways are presented in Table 380 5. The best result for each measure for a given country is in bold. It can be seen that in most cases, the proposed method achieved better performance than 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 Instead, the goal was to evaluate the proposed model with a control rate, which can then provide a basis for capturing the dynamics of infectious disease at the early stage and potentially associated with additional information for disease control. The results presented so far suggest that the proposed model captures 390 the disease transition and can be used to make reasonable predictions. One of the objectives for this study was to investigate whether and how the control rate can be associated with the mobility trend. To measure the degree of association or relationship between two variables quantitatively, correlation 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 of the tendency to vary together. A positive correlation coefficient indicates that both variables move in the same direction. For example in the financial 400 markets, a positive or negative correlation coefficient indicates two stocks move in the same or opposite direction, respectively. For this study, a positive correlation between control rate and any form of processed mobility trend will indicate that the direction of changes in control rate aligns with the changes in mobility trend. The control rates obtained in four stage predictions and the mobility trend processed by four different ways are presented in Table 5 . The number of days in the 2nd column is the data length used for prediction. The control rate was varied from 0.02 to 1.0 and the prediction was run for four data lengths and optimum rate was obtained by minimum RMSE (using MAE produced the same 410 results of rate). Notice that M c can be negative, but the control rate need to be positive, therefore in Table 5 , |M c1 | and |M c2 | were used. To assess how the association may be established between the control rate 23 Figure 8 : Results of correlation coefficients between the control rate and four types of mobility trend based on 20-day death prediction for six countries. and the mobility trend being processed in four different ways, the correlation coefficients between the rates and mobility trend were calculated. The results of correlation coefficients are given in Fig. 8 . It can be seen that the positive correlation is found between the control rates and average mobility changes |M c1 | and |M c2 |, which suggest that the change of control rates is in line with the change of |M c1 | and |M c2 |. In addition, apart from France, average change of mobility within the entire prediction period |M c2 | has a higher correlation 420 with the control rate than the rest. These results are encouraging and suggest the potential of further development for incorporating the mobility trend into the dynamic disease modelling. 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 it may not be suitable for the situation like Germany unless further modification 485 can be made with additional region-specific knowledge and data. Due to the complexity involved in infectious disease modelling, it is difficult to apply one model to suit all countries or different scenarios in real life. A better research direction may be to tailor the study for one country or target to tackle a specific scenario such that the model can be adjusted accordingly, which 490 however are beyond the scope of this study. There are future studies that may be conducted from different perspectives by employing the proposed model. For example, the current study was based on the global data published by Johns Hopkins University data repository, which unfortunately does not include the age-specific data. Some studies have been carried out using the age-specific data 495 [54] , which may be used to investigate the age-related dynamics of the proposed model as the basis for future research. This study presented a novel approach that introduced a dynamic transmission rate into infectious disease model for COVID-19. A control rate was 500 included to govern the speed of disease spreading, which can be associated to the quantifiable information related to disease control, such as mobility trend data via Apple Maps. The impact of dynamic transmission rate on the overall infection case was demonstrated by simulation. The results based on six European countries suggest that the proposed approach provided an overall improvement 505 for model fitting and mortality prediction during the early days of the pandemic. The relationship between the control rate and four types of mobility trend presentations were investigated and the results suggest that the control rate is correlated with the average mobility changes. Integration of multiple sources of data into disease modelling is a challenging task and it is difficult to 510 have a universal approach that can capture all the characteristics of infectious disease. 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