What Does Covid-19 Look Like in Vietnam?

by Anna

Introduction

The Covid-19 pandemic has greatly impacted the world, including Vietnam. Vietnam got its first two Covid cases from two Chinese men that traveled to Wuhan on January 23rd. Vietnam’s lockdown restrictions, well-developed public awareness, and an effective contact tracing method has effectively tackled the first three Covid waves, recording only under 4000 cases and 35 deaths within 96 million citizens. Vietnam hasn’t had a locally transmitted case for a few months.

However, on April 27th, 2021, a new locally transmitted Covid-19 case, caused by the recent delta variant, appeared, marking Vietnam’s fourth Covid 19 resurgence. Vietnam’s faster transmission rate and an entirely susceptible population allow the virus to quickly infect thousands of people. This disease spread that is happening now in Vietnam could be explained by exponential growth. This blog post will calculate and evaluate the exponential curve of daily Covid-19 cases in Vietnam starting from April 27th.

How is Covid-19 Growing in Vietnam?

This exponential model will represent the dependent variable n, the growth of new cases, against the independent variable t, the number of days since the outbreak. Vietnam’s Covid-19 spread could be modeled using this exponential function:

Variables:

N(t): the number of new cases on any day

N0: the initial infected population

R: the basic reproduction number

t: the total number of days since the outbreak. The change in time is represented by t-1 because the graph start plotting the initial case on April 27th at x=1

d: the infectious period

The spread of Covid-19 is dependent on the R-Value, or the basic reproduction number. This variable defines the average number secondary case that would be caused by an individual carrying the disease. The trend of Covid-19 is calculated according to this variable: if it is below one, the disease would lessen and die out; if it is one, the disease can spread, but it can be contained and won't progress into a pandemic; if it is above one, the disease is highly transmissive and could spread rapidly. Hence, in my equation, I multiplied the initial number of cases (the first few infected individuals) to the reproduction number to determine the spread of Covid-19 in Vietnam. The variable t represents the independent variable, which is the numbers of days that has passed since the discovery of the first case. This change in time is represented by t-1 because my graph starts plotting the first case on April 27th from x=1. Hence, a day needs to be subtracted to stay true to the current timeline (for day 1 (April 27th), t-1 would be 0, which would result in the one initial case that Vietnam recorded). This variable is divided by d, which represents the infectious period. There is a period between contracting the disease and becoming transmissive. It is difficult to track the number of daily cases, so this equation assumes all cases will occur in intervals, after the infectious period.

The Relationship Between Exponential Growth and Covid-19?

An exponential model can demonstrate Covid-19 growth because new cases originate from existing cases. When there are more cases, there will be more infected individuals spreading Covid-19, increasing the rate of disease spread. For instance, assume that an infected individual can spread Covid-19 to two other people. People become highly contagious two days after being infected, so covid will spread every two days. The diagram below displays the progression of Covid-19 given the assumptions:

Figure 1: The spread of Covid-19 from one infected person with a reproductive number of 2.

From figure 1, the infected population grew rapidly due to the proportional growth between transmission rate and infected people. The 1024 cases on day 20 will become 32,768 cases ten days later under the same conditions. The entire world will be infected with Covid-19 if this continues.

Variables R and d are necessary to model Vietnam’s Covid-19 situation. The variable R represents the basic reproduction number or secondary cases originated from an infected person within an entirely susceptible population. Vietnam is susceptible to the delta variant, and countermeasures were eased, so R could be determined.

To calculate R, the number of contacts per day (c) is multiplied by the probability of transmission (r) and the infectious period (p). Note how R is the secondary cases caused by an infected person, while r is the probability of transmission upon contact with Covid-19:

Vietnam’s Covid-19 transmission rate is 3.8% in high-risk areas, so a rate of 3.5% is utilized for all areas in Vietnam (link). The variant average infectious duration of nine was taken for this model (link). The contact rate was calculated using data from the World Health Organization on patients’ contact information between April 27th and May 9th, when limited countermeasures were implemented. For example, a Chinese resident diagnosed with covid on May 2nd came in contact with 52 people. The contact rate up to May 9th is:

Applying the formula above for other cases before May 9th yields an average contact rate of 8 people per day. Therefore, assuming that Vietnam is susceptible to the delta variant, and there were no lockdown until May 9th. the R-value for Vietnam is below:

The latent period between exposure and becoming positive is four days. Nonetheless, a person is infectious one and a half days before tested positive (link). Therefore, the latent period is 2.5 days. After the latent period, a person is still infectious until symptoms are present, so d is the latent period and half the infectious period, which is 7. This model assumes all cases occur after 7 days (link).

The exponential function for Vietnam’s fourth Covid-19 wave is:

From this equation, the number of new cases in Vietnam after one month without intervention will be:

Ho Chi Minh, the epicenter, could treat an estimated 30,000 patients with its current healthcare system (link). However, according to exponential growth:

In approximately three months, the number of new cases will overcome the city’s healthcare capacity. The virus would be difficult to control then as Ho Chi Minh is a city with advanced medical systems.

Exponential Graph Sketching

An exponential function demonstrating Vietnam’s Covid-19 spread is modeled on Desmos and compared with Vietnam’s daily new Covid-19 cases recorded on VnExpress. The graph will continue until October 1, 2021, when Covid-19 in Vietnam started lessening.

Figure 2: The initial exponential model for the spread of Covid-19 in Vietnam in comparison to actual records of daily new cases

The model accurately predicts the number of new cases at the beginning, portrayed through the alignment between the data in April and May and the graph. However, the exponential graph grows rapidly and becomes steeper compared to actual data. While the number of cases started decreasing around September, the exponential graph continued to progress.

To represent the data more accurately, three exponential regressions are generated by Desmos to represent three distinct periods with different reproduction rates observed in the data’s general trend.

Figure 3: The spread of Covid-19 in Vietnam, represented by three exponential regression model

The regressions are a better representation of Vietnam’s Covid-19 growth as they closely resemble the recorded data. The regressions’ R value is 1.10 on average, much lower compared to initial calculations because strict countermeasures are considered. The last regression model is decaying, indicating a decrease in Covid-19 transmission.

Will Covid Continue to Grow Exponentially?

Exponential growth can’t continue forever, as seen in figure 2. There are countermeasures a country could implement to reduce or exacerbate the reproduction rate of diseases. Preventative measures have been applied by Vietnam since May 9th , and a strict lockdown order was enforced on July 9th, banning gatherings of more than two people except for necessary business. These changes modify the transmission and contact rate, which affect the reproduction number. The R-value is not constant in the context of disease spread.

Additionally, the model doesn’t consider recovered and immune patients. Hence, an exponential model assumes the entire population is susceptible at any given time. However, as patients recover from Covid-19, they are either immune to Covid-19 or have passed away, so they are no longer contagious. The number of immune individuals will increase within the population through time. When everyone has been infected and is immune, Covid-19 stops spreading. Equally important, if Vietnam is able to achieve herd immunity through vaccination, the transmission rate would be significantly lower, preventing exponential growth from happening.

The SIR Model

An alternative model to demonstrate Covid-19 spread is the SIR (Susceptible - Infected - Recovery) model. This model also assumes that the entire population is susceptible to the disease, and there is a small population of infected people transmitting the disease. However, while exponential growth models a population that is susceptible at any time, the SIR model divides the population into three categories: Susceptible people that can become infected (S), infected people that transmit disease (I) and recovered people immune to the disease(R). The graph records changes in all three variables over time. Hence, in a SIR graph, the infected population increases at first, but the graph will decay as the recovered population increases.

Figure 3: Typical SIR Model to Represent the Spread of a Disease within a Population. Credits: C. M. Macal, Figure 1: Typical SIR model solution showing progression of population disease states for susceptible, infected, and recovered compartments. In this example, the entire population becomes infected and eventually recovers, 2011.

Conclusion

While exponential growth isn’t the best option for graphing disease spread, it is helpful in determining the growth in the early stages and projects future developments if no actions are taken. From the growth presented, people can make decisions that would impact the exponential curve in the future and “flatten the curve”. In Vietnam’s case, the country has implemented strict lockdown restrictions where unessential businesses are closed off, and people have to wait for soldiers to deliver food to their houses. In the meantime, the country also boosts vaccination to quickly achieve herd immunity (link). From the measures above, Vietnam has seemed to successfully mitigate the pandemic to a certain extent, managing to change the trajectory of the curve.

Credits

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