Evaluating the Impact of Social Distancing on COVID-19 Spread in Vietnam by using Logistic Growth Curve Model

The regular increase in COVID19 cases and deaths has resulted in a worldwide lockdown, quarantine and some restrictions. Due to the lack of a COVID-19 vaccine, it is critical for developing and least developed countries like Vietnam to investigate the e cacy of non-pharmaceutical treatments like social distance or national lockdown in preventing COVID-19 transmission. To address this need, the goal of this study was to develop a clear and reliable model for assessing the impact of social distancing on the spread of coronavirus in Vietnam. For the case study, the Logistic Growth Curve (LGC) model, also known as the Sigmoid model, was chosen to t COVID-19 infection data from January 23, 2020 to April 30, 2020 in Vietnam. To determine the optimal set of LGC model parameters, we used the gradient descent technique. We were pleasantly surprised to discover that the LGC model accurately predicted COVID-19 community transmission cases over this time period, with very high correlation coe cient value r = 0.993. The results of this study imply that using social distancing technique to atten the curve of coronavirus disease infections will help minimize the surge in active COVID-19 cases and the spread of COVID-19 infections.

19 cases and deaths has resulted in a worldwide lockdown, quarantine and some restrictions. Due to the lack of a COVID-19 vaccine, it is critical for developing and least developed countries like Vietnam to investigate the ecacy of non-pharmaceutical treatments like social distance or national lockdown in preventing COVID-19 transmission. To address this need, the goal of this study was to develop a clear and reliable model for assessing the impact of social distancing on the spread of coronavirus in Vietnam. For the case study, the Logistic Growth Curve (LGC) model, also known as the Sigmoid model, was chosen to t COVID-19 infection data from January 23, 2020 to April 30, 2020 in Vietnam. To determine the optimal set of LGC model parameters, we used the gradient descent technique. We were pleasantly surprised to discover that the LGC model accurately predicted COVID-19 community transmission cases over this time period, with very high correlation coecient value r = 0.993. The results of this study imply that using social distancing technique to atten the curve of coronavirus disease infections will help minimize the surge in active COVID-19 cases and the spread of COVID-19 infections.

Introduction
The COVID-19 pandemic was rst identied in the Chinese city of Wuhan, Hubei Province [1]. COVID-19's appearance coincided with the Lunar New Year holiday, China's most festive time of year [2]. During this special and long-awaited holiday, a large number of Chinese citizens returned home. Approximately 5 million people left Wuhan, the epicenter of the COVID-19 pandemic, according to [3]. Approximately onethird of those people traveled outside of Hubei province. Because of the global nature of travel, they could have spread the virus inside China and to other countries [2].
Since COVID-19 spreads mainly from person to person who are in close physical contact (less than 6 feet of distance) for an extended period of time [4], social distancing is a measure to minimize pandemic spread by reducing face-to-face contact with others [5]. 1 Several previous studies, as summarized above, simulated and forecast the outbreak's path using models ranging from extremely simple to complex with a large number of variables and parameters. Table 1 summarizes some of the advantages and disadvantages of the aforementioned methods. However, a simple and effective methodology for measuring and evaluating the ecacy of social distancing techniques in preventing the COVID-19 pandemic remains undeveloped. The methodology is applicable to seasonal and nonseasonal models, and outliers can be treated eectively When there are shifts in observation and modications in model specication, the model becomes unstable Sigmoid functions have gained popularity in deep learning as an activation mechanism in an articial neural network [24]. Sigmoid functions are also useful in a wide variety of machine learning applications that include the conversion of a real number to a probability [25]. When used as the nal layer of a machine learning algorithm, the sigmoid function can be used to transform the model's output to a probability score, which is often easier to deal with and interpret. Another use of the sigmoid equation is discussed in this article: population growth modeling.
In general, a novel contagious pathogen to which a population lacks immunity can spread exponentially in the early stages, when the supply of susceptible individuals is abundant. COVID-19 was caused by the SARS-CoV-2 virus, which grew exponentially early in the process of infection in many countries in early 2020 [26]. Due to a variety of causes, including a lack of susceptible (either through continued infection spread before it reaches the threshold for herd immunity or through physical distancing policies), exponential-looking disease curves may rst linearize and then reach a maximum limit [27].
A sigmoid function can be used descriptively or phenomenologically since it ts perfectly not just with the initial exponential growth, but even with the pandemic's subsequent leveling o when the populace gains herd immunity. This contrasts with actual pandemic models, which seek to formulate a description based on the pandemic's dynamics (e.g. contact rates, incubation times, social distancing, etc.).

1.3.
Our contribution The aim of this study is to demonstrate that the Vietnamese government's country social distancing policies would have a crucial and important eect on slowing the spread of the coronavirus and eventually suppressing it. We examine the COVID-19 outbreak's prevalence in Vietnam using real-time occurrence data and a compartmental mathematical model, as well as a logistic growth curve model.
Gradient Descent is a well-known optimization method in Machine Learning and Deep Learning, and it can be used for the majority of learning algorithms [28,29,30,31]. In this work, Gradient Descent is used to estimate the values of parameters of the sigmoid function that minimizes a least square cost function. More specifically, we present the ndings of an analysis of COVID-19 cases in Vietnam before and after social distancing measures. The data indicate that daily cases declined after the lockdown, implying that the lockdown interventions have been eective in suppressing the disease so far.

Organization of paper
The following is the organization of the paper. The materials and method are presented in the second section. Section 3 describes the results and discussions. Finally, section 4 gives some conclusions. Vietnam, a neighboring nation of China, recorded the rst case of COVID-19 on January 23, 2020 [32]. Two Chinese men were found to be infected with the coronavirus and were treated at the Cho Ray hospital in Ho Chi Minh City, Vietnam. Since then, the government has imposed plenty of public-health measures to combat the outbreak. The data used in this study was obtained from the Vietnamese Government information channel, which was published by Vietnam News Agency (https://baotintuc.vn/) as well as [33]. We created a dataset by combining data from both sources from January 23, 2020 to April 30, 2020. The data used in the modeling is dened in Appendix A. The dataset contains the number of new conrmed COVID-19 imported cases and local transmission cases on a daily basis, as seen in Fig. 1. The COVID-19 case pattern in Vietnam is depicted in Fig.  2. We concentrate on COVID-19 cases reported in the community.

Method
An Logistic Growth Curve (LGC) was used in our research to analyze and model the growth of COVID-19 infections in Vietnam [34].
LGC is an S-shaped sigmoidal curve that increases growth in the beginning period, but reduces growth later on. In logistic growth, a population's per capita growth rate decreases as population size reaches a threshold imposed by scarce LGC is dened by the following equation: wherein: y is the cumulative number of infections occurring at a certain time t; K is referred to as the "Carrying Capacity"; a, b are the parameters that determine the form of the curve; The least square error (LSE) [35] was used in this study, which dened the cost function as: where θ is a parameter vector (a, b) to optimize; y (i) is the cumulative number of conrmed cases at a particular point in time t (i) ; n is the number of data points; and h θ (t (i) ) is the projected total number of conrmed cases at a certain time t (i) for a particular θ based on Eq. (1). The goal is to discover values that gives minimum cost value when the predicted value and the actual data are close to each other, as determined in Eq. (2).
To achieve the objective, we employ a gradient descent-based iterative method. (i.e. Python's Trusted Region algorithm is used in this case) to determine the appropriate value θ to achieve LSE in Eq. (2) for data tting [36]. Also, the gradient descent is a computationally ecient method. It is well-known that the gradient descent algorithm for univariate function only needs a linear computational complexity O(kn), where k is the number of iteration and n is the number of data.
Regularly, when the date is determined, K is used as the total population. Alternatively, the value of K is not constant in the COVID situation and continues to grow larger day by day.
To determine an acceptable value for K, we follow Meyer and Ausube's procedure [37] in the process of optimization/iteration. If a sequence of data is provided, estimating the value of K is also straightforward since the model can forecast the growth rate.
A drawback of the gradient descent is that it is an iterative approach for seeking function's local minima. It does not always nd the global minimum and may become trapped at a local minimum. Nonetheless, we found that the numerous alternative sets of parameters in our gradient descent method of LGC model all provided a good t of the data and their dierences were neglectable. We speculate that for a simplistic univariate model like LGC, our local minima of gradient descent may be very close to the global minimum. 3.
Results and discussions

Results
The LGC model was tted to the available data in this study to determine the ecacy of social distancing policies in containing the spread of COVID-19 in Vietnam.
To assess the impact of social distancing on disease prevention, we collected data over a 99day period beginning with the outbreak of the epidemic in Vietnam. This data is used to approximate the parameters of the logistic model. The total number of actual and expected cases overlapping is shown in Fig. 3. Our tted infections in Fig. 3 were very close to the observed data of infections. They have a very strong Pearson's correlation coecient (r = 0.993) [38] when plotted against each other, as shown in Fig. 4. This demonstrates the importance of social distancing interventions in reducing the overall number of infections in the community exponentially. Figure 5 depicts the progression of the epidemic in Vietnam, as well as the eects of the logistic model, from its inception to the day when the government implemented social distancing policies. The gure represents the number of COVID-19 infections in the community and the estimated number of conrmed cases based on the logistic model being similar to each other. This demonstrates the pandemic's risk, as the number of conrmed COVID-19 cases in the population grows exponentially.
Finally, as shown in Fig. 6, the total number of actual infections increased gradually over 120

Discussions
Vietnam slowly lifted social distancing policies and movement restrictions on May 8, 2020, after being closed for nearly a month [39]. On 19th May 2020, Vietnam was one of the few countries to enter the normal situation at the earliest [40]. As shown in Fig. 7, several international media organizations praised Vietnam for its exceptional performance in combating the COVID-19 pandemic at the time. The Financial Times, one of the world's leading newspapers, published an article on March 24, 2020, highlighting that Vietnam's coronavirus defense deserves praise for a low-cost model [41]. Social distancing appears to have been a factor in limiting the mass spread of COVID-19 infection in Vietnam, as shown by this research. The impo- The actual data in the period of 120 days from the beginning of the outbreak and the predicted growth of COVID-19 infection in Vietnam. (Notes: LGC1 estimated with data before social distancing day, parameters a = 23163220.203, b = 0.052, c = 65345425.117 and LGC2 estimated with data before and after social distancing day, parameters a = 278.347, b = 0.091, c = 152.582). sition of social distancing had averted the worstcase scenario of the pandemic. It has aided the Vietnamese government in attening the infection curve through the collaboration of various agencies and the general public. It is important to understand that social distancing is not intended to eradicate COVID-19 entirely; rather, it is intended to atten the curve, minimize an increase (or tall curve) in infections or the number of reported active COVID-19 cases. This is to ensure that a country's health systems are safe and prepared to deal with a pandemic.

Conclusions
COVID-19 vaccines are rare, hence it is vital for underdeveloped nations like Vietnam to study other means of avoiding COVID-19 spread, such as social distance or national lockdown. This paper has presented a reliable model representing the impact of social distancing on the spread of coronavirus in Vietnam.
Our data analysis revealed that there was an exponential rise in the number of coronavirus cases in the population, then the growth was

V i e t n a m 's s u c c e s s i n C O V I D -1 9 l o c k d o w n
Suffering no deaths from the virus and had limited total infections to just 288, despite being next door to China. Vietnam has been widely praised for its success in tackling COVID-19.
Despite its border with China, low income and population of 95 million, Vietnam is an outlier success story in the pandemic. It has 270 confirmed cases of the virus and no deaths.
When the health care systems of most powerful countries in the world have failed to curb the spread of COVID-19, Vietnam performed an outstanding work against the pandemic.
International media has praised Vietnam's handling of the crisis, which has resulted in relatively few cases and not on death, considering Vietnam neighbors China.
Vietnam chose to prevent rather than fight Covid-19, a strategy which means it has had no virus deaths.
Even if we consider these numbers with a dose of caution, one thing is clear: Vietnam has a done a good job thus far in fighting the coronavirus.
Vietnam is a lower-income, densely populated country that shares a large land border with China, where the outbreak first began. [46] Hutt, D. (2020), Some thoughts on Vietnam`s Covid-19 repression.