ISSN (print): 1978-1520, ISSN (online): 2460-7258
DOI: https://doi.org/10.22146/ijccs.73334 ◼ 1
SVEAuAdIR model of COVID-19 Transmission
Anindhita Nisitasari*1, Nur Rokhman2
1Master Program of Computer Science, UGM, Yogyakarta, Indonesia,
2Department of Computer Science and Electronics,UGM, Yogyakarta, Indonesia e-mail: *1anindhita.n@mail.ugm.ac.id, 2nurrokhman@ugm.ac.id
Abstrak
Pandemi COVID-19 yang terjadi telah menjadi perhatian dunia karena cepatnya tingkat penyebaran wabah dan banyaknya kasus kematian yang terjadi. Tujuan penelitian ini adalah membangun model SVEAuAdIR, mengetahui penyebaran COVID-19 di Indonesia melalui prediksi penyebaran penyakit, dan mengetahui pengaruh adanya vaksinasi yang dilakukan dengan melihat bilangan reproduksi dasar dari model SVEAuAdIR. Hasil yang diperoleh dari MAPE pada model sebesar 12%. Sehingga dapat dikatakan model SVEAuAdIR baik digunakan untuk model prediksi penyebaran COVID-19. Keadaan yang sudah tidak ada lagi individu terinfeksi COVID-19 disebut bebas penyakit COVID-19, dengan demikian diprediksi bahwa Indonesia bebas COVID-19 pada tanggal 7 Oktober 2021. Target dari Kementerian Kesehatan Indonesia yaitu pada akhir tahun 2021 penyebaran penyakit COVID- 19 dapat dihentikan. Namun, pada tanggal 7 Oktober 2021 dilihat dari data aktual selama penelitian ini berlangsung, masih terdapat kasus baru COVID-19. Pada hari tersebut tercatat 1393 kasus baru yang terinfeksi COVID-19. Dengan demikian, menunjukkan bahwa target Indonesia bebas penyakit COVID-19 pada akhir tahun 2021 tidak tercapai. Bilangan model SVEAuAdIR berada pada range nilai , yang memiliki arti bahwa penyebaran penyakit mendekati bebas penyakit. Berdasarkan hasil nilai model SVEAuAdIR penelitian ini disimpulkan bahwa dengan pemberlakuan vaksinasi dapat menurunkan tingkat penyebaran COVID-19 dibandingkan dengan yang tidak melakukan vaksinasi.
Kata kunci— COVID-19, SVEAuAdIR, Prediksi
Abstract
The COVID-19 pandemic that has occurred has received worldwide attention due to the rapid rate of transmission of the outbreak and the large number of deaths that occurred. The aim of this study is to build the SVEAuAdIR model , determine the transmission of COVID-19 in Indonesia by forecast the spread of the disease, and determine the effect of vaccination by looking at the basic reproduction number of SVEAuAdIR model. The results obtained from MAPE on the model are 12%. So it can be said that the SVEAuAdIR model is good for prediction models for the spread of COVID-19. The situation where there are no more individuals infected with COVID-19 is called COVID-19 disease free, thus it is predicted that Indonesia will be free of COVID-19 on October 7, 2021. The target of the Indonesian Ministry of Health is that by the end of 2021 the spread of COVID-19 can be stopped . However, on October 7, 2021, judging from the actual data during this research, there were still new cases of COVID-19. On that day there were 1393 new cases infected with COVID-19. Thus, showing that Indonesia's target of being free of COVID-19 disease by the end of 2021 has not been achieved. The number of the SVEAuAdIR model is in the range of values , which means that the spread of disease is close to disease-free. Based on the results of the value of the SVEAuAdIR model, this study concluded that vaccination could reduce the spread of COVID-19 compared to those who did not vaccinate.
Keywords— COVID-19, SVEAuAdIR, Forecasting
1. INTRODUCTION
The COVID-19 pandemic has come to the world's attention due to the rapid rate of spread of the outbreak and the number of deaths that occur. According to the World Health Organization (WHO), the ongoing spread of COVID-19 is occurring through people infected with the coronavirus. When a person infected with this virus causes symptoms such as high fever, shortness of breath, sneezing or coughing, sometimes accompanied by a loss of sense of taste or smell. The virus is easily spread through small droplets in the nose or mouth [1].
There is a lot of evidence where machine learning algorithms have been shown to provide efficient predictions in healthcare[2][3]. Nsoesie [4], has provided a systematic review of the approaches used to forecast the dynamics of influenza pandemics. They have reviewed research papers based on deterministic mass action models, regression models, predictive rules, Bayesian Networks SEIR models, ARIMA forecasting models etc. Recent studies on COVID- 19 include only exploration analysis of available limited data. The SEIR model is a mathematical approach model developed and widely used for some infectious diseases to look at the dynamics of population spread due to these infectious diseases[5]. The model was implemented by several researchers for the spread of COVID-19 [6]–[8]. The model was developed for the spread of COVID-19 disease with attention to vaccination [9], [10]. Factors of groups of individuals who have been vaccinated are strongly considered for further investigation. COVID-19 vaccine that has been spread, especially in Indonesia requires monitoring or case studies on the effects of vaccines on the spread of COVID-19.
The SEIR model needs to be modified taking into account a group of vaccinated individuals hereinafter referred to as SVEAuAdIR. The model can be formed by estimating the value of parameters based on the characteristics of the spread of COVID-19 disease. The SVEAuAdIR model is a problem of initial values with the usual form of one-order differential equation systems so that a solution is needed with a numerical approach. Ordinary differential equations can be solved by several methods, one of which is the Runge-Kutta method of the fourth order. This method has been used in several studies on the spread of COVID-19 [11].
However, the research has not considered the existence of vaccinated groups of individuals. The Fourth-order Runge-Kutta method is an alternative method of the Taylor series method that does not require derivative calculations. The advantages of this method have a higher accuracy than the Euler method, Heun method and Taylor series method. This method has a disadvantage that the higher the order, the more it has the number of iterations. In the Runge Kutta method the highest order is the fifth order [12]. The Runge-Kutta method was chosen in the order of four because the approximate value obtained will be close to the exact value and the number of iterations is expected to be less. [13].
2. METHODS
The step used in this study predict the number of individuals on the SVEAuAdIR model using the Runge-Kutta method of the fourth order in the Indonesian population, starting from the collection of data on the number of individuals of SVEAuAdIR COVID-19 disease for 1 year. Then from the data, the process of training data is carried out. In the training process the data produces estimates of the number of individuals of each group on the SVEAuAdIR Model and the estimated value of parameters. After obtaining the estimated value and the SVEAuAdIR Model is built, then testing the data on the model, an analysis of the predicted value produced.
The next step in testing data is to calculate the value in order to determine at what phase the spread of the disease is occurring. Then, calculations are performed for error values on the model and check the performance of the model based on accuracy using MAPE. If the model shows a MAPE value of less than 90% then it can be said that the model succeeded. If MAPE model results more than 90% of models are said to fail and the final process of this study is to implement the predictive results of the SVEAuAdIR model.
2.1 Data Source
The data used in this study was taken from the Indonesian Health Profile [14] in the form of annual data on the number of Indonesians and from WHO [15] obtained data on the number of individuals infected due to COVID-19. Annual data of crude birth rate (CBR), crude death rate (CDR) were obtained and incidence rate as well as COVID-19 death rate obtained from COVID-19 Dashboard by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU) [16]. Daily data on the number of individuals who recovered, died, and the number of vaccinated individuals were taken from kawalCovid19.id [17].
2. 2 SVEAuAdIR Model
The purpose of this study was to analyze the effects of vaccine administration and to predict the spread of COVID-19 that occurred in Indonesia. To achieve this goal, our model must consider vaccinated individuals as parameters that describe vaccination interventions. To achieve this, the human population divided it into seven categories based on their health status.
group of healthy individuals but susceptible to infection with the disease (susceptible / S), group of vaccinated individuals (V), groups of individuals who have been infected with COVID-19 but have not been able to transmit to other individuals (exposed / E) Furthermore, the group of individuals who have been infected and able to transmit but not detected by the government (asymptomatic undetected / Au), the group of infected individuals are also able to transmit but detected by the government (asymptomatic detected / Ad), a group of individuals who have symptoms and are hospitalized (infected / I), groups of individuals who recover with temporary immunity (recovered / R ). ). The number of individuals S, E, Au, Ad, I, and R at time t is S(t), V(t), E(t), Au(t), Ad(t), I(t), and R(t), so the number of individuals in the population at time t is
The assumption given to the model is a homogeneous population, a rapid test given for identification of a population and given to individuals who show no symptoms and performed to all groups of individuals except I. Au individuals can socialize more than indivudu I and Ad because there are no symptoms. People who are in the hospital recover faster due to the limited number of beds or other medical resources in the hospital. It is assumed that additional recovery rates for infected individuals in the hospital. Thus the momentary change of the number of each individual group can be written in full for the SVEAuAdIR model as.
(1) which is a first order nonlinear differential equations system, provided that the initial
non-negatif condition value is assigned to
S(0)≥0,V(0)≥0,E(0)≥0,Au(0)≥0,Ad(0)≥0,I(0)≥0,R(0)≥0. Parameter Λ,β,μ, dan ϕ each is the rate of birth naturally, the rate of infection, the rate of natural death, and the death rate due to COVID-19. Parameter ξ_i and ξ_a represent a reduction from I and Ad respectively because
there is isolation at home or in the hospital. Further and each showed the rate of development of COVID-19 based on the incubation period, natural recovery rate, and temporary loss of immunity. Note that p describes the proportion of exposed individuals who have progressed to asymptomatic individuals, whereas b is the rate of hospital capacity or the number of medics. is the rate of improvement in natural recovery due to hospital treatment, is the level of hospitalization from Ad to I, and is the necessary effort for early detection of COVID- 19 infection. Parameter is the rate of vaccination and the rate of immunity is . A transmission diagram to state the spread of disease to a model that has been built is shown in Figure 1.
Figure 1 Transmission of COVID-19 SVEAuAdIR Model diagram
The solution of the SVEAuAdIR model to equation (1) is function S(t), V(t), E(t), Au(t), Ad(t), I(t), and R(t). Each of these functions shows the number of individuals S, V, E, Au, Ad, I, and R at the time of t. The number of individuals is represented into graphs that form a particular pattern. Thus the pattern of spread of disease is a pattern formed from the completion of the SVEAuAdIR model.
2. 3 Fourth Order Runge-Kutta Method
In the SVEAuAdIR model that pays attention to vaccinated groups of individuals, it is a matter of initial value with the usual form of one-order differential equations. The problem can be solved numerically using the Fourth Order Runge-Kutta method. According to Atkinson [18], Fourth Order Runge-Kutta formula to determine the solution of the initial value problem system can be written as
with
2. 4 MAPE
Performance on the model can be tested for accuracy using Mean Absolute Percentage Error (MAPE) on available COVID-19 data sets. Mape formula that is
where, y_i is actual value, y ̂_i as predictive value, and n indicates the number of data points. By definition, the lower the value of this performance metric, the better the performance of the forecasting model [19].
Based on Lewis [20], MAPE values are interpreted into 4 categories MAPE <10%, the results of predictions mean very accurate
MAPE 10-20%, good prediction results
MAPE 20-50%, the prediction results are still reasonable MAPE >10%, weak or inaccurate prediction results 2.5 Basic Reproduction Number
The R_0 value indicates about the transmission of the disease. This is the fundamental goal of epidemiologists studying new cases [21]. In simple terms, R_0 determine the average number of people who can be affected by one person being infected over a period of time. If the value of R_0<1, means the spread is expected to stop. If the value R_0=1 means the spread is stable or endemic. If the value R_0>1 indicates the spread is increasing without intervention.
The value of R_0 SVEAuAdIR model can be calculated by the formula in equation 2 below
(2)
3. RESULTS AND DISCUSSION
This study uses CelebA images as a dataset, totaling 202.599 images. This dataset is then divided into training, validation, and testing data. CelebA dataset has a large number of images, the experiment is divided into 5 batches, they are A1 with 10% of the total dataset, A2 with 20% of the total dataset, A3 with 50% of the total dataset, A4 with the number data 70% of the total dataset and A5 uses 100% of the total dataset.
The results are shown into qualitative and quantitative result. Qualitative results are the comparison of generic images with the original HR images shown in Figure 2 and the comparison of more clearly detail shown in Figure 3. Each rows in Figure 3 compared different detail. The first and the last row demonstrate detail of eye with glasses and without glasses. The middle row demonstrates detail of edge information. Comparison in Figure 3 show that our CGAN model can generate high frequency information and reconstruct tiny detail features.
Figure 2 Qualitative Comparison with CelebA Dataset (4x upscaling factor)
LR CGAN HR
Figure 3 Comparison of Image’s Detail
Quantitative results are the comparison of PSNR and SSIM values for each experiments shown in Table 1 using validation dataset and Table 2 using testing dataset. Quantitative results is also used for the comparison of PSNR and SSIM values with a previous study shown in Table 3.
Table 1 Quantitative Comparison Using Validation Dataset
Experiment Number of Images Quantitave Value of Image
PSNR SSIM
A1 1.013 26,036 0,923
A2 2.026 26,346 0,927
A3 5.065 26,553 0,931
A4 7.091 26,646 0,931
A5 10.130 26,634 0,931
Table 2 Quantitative Comparison Using Testing Dataset
Experiment Number of Images Quantitave Value of Image
PSNR SSIM
A1 1.013 24,564 0,909
A2 2.026 24,507 0,906
A3 5.065 24,50 0,907
A4 7.091 24,501 0,907
A5 10.130 24,507 0,906
Table 3 Comparison of PSNR and SSIM Value with The Previous Study Number of Image Size of Input Image Quantitave Value of Image
PSNR SSIM
10.000 32,66 0,863
10.130 24,51 0,906
Features contained in input image can be lost when using multi-layer convolutional nework (CNN). Model also can not reach the performance of the model with skip-connection, although increasing training iteration. It means that skip-connection can keep useful information, even though deep convolutional network can not recover in the next layer [12].
This study uses skip-connection to improve the performance of the CGAN model and accelerate conversions during the training process. The training curve is shown in the graph of generator and discriminator network loss using skip-connection during the training process. The X coordinate shows the iteration during the training phase (with the number of epochs being 10) and the Y coordinate shows the value of the generator and discriminator network loss functions.
The training process uses the same number of epoch in each experiment. Figure 4 and 5 shows the training curve using 10% and 20% of the total dataset. Figure 6 and 7 shows the training curve using 50% and 70% of the total dataset. Figure 8 shows the training curve using 100% of the total dataset.
A1
Figure 4 The Training Curve of A1 Experiment
A2
Figure 5 The Training Curve of A2 Experiment
A3
Figure 6 The Training Curve of A3 Experiment
A4
Figure 7 The Training Curve of A4 Experiment
A5
Figure 8 The Training Curve of A5 Experiment
The number of dataset affect loss value of generator and discriminator, as seen from above training curve. Figure 4 shown that loss value of generator and discriminator are
relatively bigger when the training process uses a small number of dataset. however loss value are relatively smaller when the training process uses a bigger number of dataset, shown in Figure 8.
Generator produce a relatively real image during training process, so that discriminator can not distinguish between generated image and real image. It means that d-loss will increase, but discriminator will optimize and reduce d-loss in the next training process. Discriminator and generator will reach a balance when generator produce pseudo real images and discriminator can not distinguish them.
4. CONCLUSIONS
This study uses a Conditional Boundary Equilibrium Generative Adversarial Network to increase image resolution and produce super-resolution images. The used size of the input image is 4x smaller than previous studies, with the same size as the output image as the previous study. Although the output image that is produced in this study is not too high resolution, the resulting image has been able to represent the original image. Also, during the training process, the generator and discriminator networks have been able to show good and stable performance.
The evaluation process uses a validation dataset and can produce an SSIM value of up to 93%.
While the SSIM value generated in the evaluation process using dataset testing reaches a value of 90%. The obtained SSIM value in this study increased by 14% from the previous study.
ACKNOWLEDGMENTS
This study has done in Laboratorium Komputer Dasar of The University of Gadjah Mada, using Graphic Card is NVIDIA GeForce GTX 1080.
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