 Research note
 Open Access
 Published:
Impact of early detection and vaccination strategy in COVID19 eradication program in Jakarta, Indonesia
BMC Research Notes volume 14, Article number: 132 (2021)
Abstract
Objective
Several essential factors have played a crucial role in the spreading mechanism of COVID19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several nonpharmaceutical interventions. Because of the rapid spread of COVID19 worldwide, understanding the significance of these factors is crucial in determining whether COVID19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID19 considering mentioned factors.
Results
Infection detection and vaccination have the potential to eradicate COVID19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID19 vaccine potential.
Introduction
At the end of 2019, a novel coronavirus disease was found in Wuhan, China. This disease, commonly known as COVID19, is caused by the wellknown Severe Acute Respiratory Syndrome Coronavirus 2 [1]. The World Health Organization first declared COVID19 as a threat to the international community on January 30, 2020, and then as a pandemic on March 11, 2020 [2, 3]. As of November 26, 2020, more than 60 million people have been infected by COVID19, with approximately 1.4 million deaths. The top five countries with COVID19 incidences, in order, are the USA, India, Brazil, Russia, and France [4]. The debate whether this virus originated from bats continues [5].
COVID19 spreads among the human population through humantohuman transmission, direct contact with an infected individual, touching a surface that contains the virus, and inhaling free droplets produced by infected individuals [6, 7]. The development and approval of a vaccine for COVID19 to protect susceptible individuals remains in progress in several countries. Hence, at this time, the most popular intervention to prevent the rapid spread of COVID19 is through nonpharmaceutical interventions including face masks, social distancing, rapid testing, contact tracing, quarantining, and maintaining individual hygiene [8,9,10,11].
Numerous researchers from diverse disciplines have contributed to the study of COVID19, from the development of a medicines, understanding the spreading mechanism, and forecasting the possible outcome if specific interventions are implemented [8, 9, 12,13,14]. Recently, many countries have been starting the intervention of vaccination to control the spread of COVID19. To predict this scenario, several authors have been introduced their model to answer this problem, such as [15, 16]. Indonesia first implemented the COVID19 vaccine massively in January in Jakarta, with the initial target being health workers and public servants. Motivated from the literature above, we wish to analyze the influence of two existing scenarios in the city of Jakarta, namely the contact tracing and rapid testing, and one new intervention, a vaccination strategy. We construct the proposed model using a wellknown compartmental model as a system of nonlinear ordinary differential equations. We then analyze the qualitative behavior of the proposed model regarding the equilibrium and stability criteria and how the basic reproduction number can be used as an indicator to determine whether the disease is eradicated or persists in the population. Using the bestfit parameter to the proposed model with incidence data from the city of Jakarta, Indonesia, we show how far we can rely on vaccination strategy to relax the social distancing policy or even eradicate COVID19 spread from the population.
Main text
Methods
Virtually all countries in the world are eagerly awaiting the availability of an effective vaccine to combat the spread of COVID19. A vaccine must fulfill at least two requirements before it can be widely used in humans. The first is that the vaccine must be safe for all population types (age, sex, race). The second is that the vaccine must demonstrate acceptable efficacy against the pathogen. There are numerous challenging aspects to the implementation of a COVID19 vaccine; one is the magnitude of the intervention required to address a sufficient population such that herd immunity in the population can be achieved. To answer this question, we must analyze the impact of a vaccination before it is actually implemented in the field. One approach is the use of a mathematical model to predict the effect of the vaccine on the population.
A flow chart of the dynamics of the proposed model is shown in Fig. 1a. We consider several important factors including detected and undetected cases, contact tracing and rapid testing to find undetected cases, quarantining to avoid further possible infection from the detected infected individuals, and vaccination strategy to minimize successful contact probability. To accommodate these factors, we divide our population based on their health status as follows: individuals who are vulnerable to COVID19 (S), vaccinated individuals (V), detected and undetected exposed individuals (\(E_u\) and \(E_d\), respectively), asymptomatic and symptomatic individuals (A and I, respectively), quarantined (Q) and recovered individuals (R).
Based on the aforementioned explanation, the mathematical model for COVID19 spread, considering contact tracing, rapid testing, symptomatic/asymptomatic cases, and quarantine intervention, is expressed by the following system of ordinary differential equations.
Description of all parameters given in Table 1. Parameter were estimated using the incidence data in Jakarta in the early spreading period of COVID19, and the result is given in 1(b). In the above model, we assume that all newborns (\(\Lambda \)) are healthy. Vaccination is given only to S with a rate of \(u_3\) which will transfer them into V. It is assumed that the vaccine has a validity period of \( \eta ^{1}\) and does not protect people perfectly from COVID19. Hence, vaccinated individual may get infected by COVID19, but the transmission rate \(\beta \) were reduced by \(\phi \). Due to contact trace \(u_1\), new infected individual separated into detected \((E_d)\) and undetected \((E_u)\) class. The undetected case \(E_d, A\) and I can be traced by the rapid/swab test intervention with the rate of \(u_3\). Our model assumes that the detected cases from A and I will be forced to conduct quarantine until they get recovered from COVID19.
COVID19 free equilibrium and the basic reproduction number
Model 1 has one trivial equilibrium, namely the COVID19 free equilibrium, which is given by
The total population at \(E_0\) is \(\frac{\Lambda }{\mu }\). In Model 1, the susceptible population is separated into nonvaccinated and vaccinated populations. The ratio is given by
It can be observed that this ratio is directly proportional to the rate of vaccination \(u_3\) and inversely proportional to the vaccination period \(\eta \). Hence, except only relying on massive vaccination rate on to the population, the policy maker also should consider the vaccine duration that will be used in the field.
Next we calculate the basic reproduction number of system (1). Let us define the transition (F) and transmission (V) matrix of system (1) evaluated at \(E_0\) as follows.
Since we have three zero rows on F, the next generation matrix of system (1) is taken by the spectral radius of \(NGM = E^TFV^{1}E,\) where \(E=\left[ \begin{array}{ccccc} 1&{}0&{}0&{}0&{}0\\ 0&{}1&{}0&{}0&{}0 \end{array} \right] ^T\). Therefore, the basic reproduction number of system (1) is given by
and \({\mathcal {R}}_0^{'} = (1u_1) \beta B + u_1 {\frac{\Lambda \,\beta \,\xi _{{2}} \alpha }{\mu \, \left( \alpha +\mu \right) \left( \mu +\delta +\zeta . \right) }},\) with \(B = {\frac{q\,\alpha \,\Lambda }{\mu \, \left( \mu +\delta +\zeta +u_{{2} } \right) \left( \alpha +\mu +u_{{2}} \right) }}+{\frac{\,\Lambda \,\xi _{{1}} \left( 1q \right) \alpha }{\mu \, \left( \mu +\delta +\zeta + u_{{2}} \right) \left( \alpha +\mu +u_{{2}} \right) }} + {\frac{\, \Lambda \,\xi _{{2}}\alpha \,u_{{2}} \left( \delta +2\,\mu +\zeta +u_{{2}}+ \alpha \right) }{\mu \, \left( \alpha +\mu \right) \left( \alpha +\mu +u_ {{2}} \right) \left( \mu +\delta +\zeta +u_{{2}} \right) \left( \mu +. \delta +\zeta \right) }}.\) The following results follows from Theorem 2 in [21]
Theorem 1
The COVID19 free equilibrium point of model 1 is locally asymptotically stable if \({\mathcal {R}}_0<1\), and unstable if \({\mathcal {R}}_0>1\).
Please note that \({\mathcal {R}}_0^{'}\) is the basic reproduction number of system (1) where no vaccine intervention implemented. From the expression of \({\mathcal {R}}_0^{'}\), it can be observed that \({\mathcal {R}}_0 < {\mathcal {R}}_0^{'}\) because \(K:=\frac{\phi u_3 + \eta + \mu }{u_3 + \eta + \mu }<1\). The higher the quality of the vaccine (smaller value of \(\phi \)), the smaller is the value of K. The parameter K represents the effect of vaccine implementation in reducing the initial basic reproduction number, which depends on the rate of vaccination and quality of the vaccine. Hence, it can be concluded that the implementation of a vaccination at a constant rate \(u_3\) reduces the basic reproduction number by K percent.
Results
According to Theorem 1, there is a chance that COVID19 could be eradicated from the community if \({\mathcal {R}}_0\) is less than unity. Because the partial derivative of \({\mathcal {R}}_0\) with respect to the contact tracing parameter \(u_1\) given by
is always negative, we can conclude that increasing the intensity of contact tracing in the community can reduce the value of the basic reproduction number. Hence, there is an acceptable probability that COVID19 could be eradicated from the community if the contact tracing effort is increase. From it can be stated that the total number of infected individuals (exposed, asymptomatic, symptomatic, and quarantine) is inversely proportional to contact tracing intervention. It can be observed that with more intense contact tracing in the field, the outbreak could be reduced significantly, and the time of the occurrence of the outbreak could be delayed for a significant period.
The results regarding the rapid testing intervention are as follows. Because
is always negative, we can observe that increasing the intensity of rapid testing to identify the undetected cases in the field and force them to conduct selfisolation could increase the probability of eradicating COVID19 from the population. It is evident from the dynamics of the total infected individuals, that the intervention of rapid testing demonstrated similar qualitative results. However, please note that rapid testing is more sensitive in reducing the number of infected individuals compared to the intervention of contact tracing. To increase the positive results of the rapid testing in the population, not only should the number of tests be increased but also rapid testing sampling must be conducted immediately on the target.
Furthermore, we can observe that
is always positive, which indicates that reducing the success transmission rate could reduce the basic reproduction number linearly. This parameter depends on the duration and intensity of the contact, and the ease of the virus spread through susceptible individuals from infected individuals. Hence, to reduce secondary infection, it is necessary to reduce the contact rate. This can be accomplished through massive social distancing or even conducting lockdowns in endemic areas. However, this intervention comes at a high cost, not only from an epidemiological point of view but also from the social and economic points of view. As an alternative, reducing the infection rate can be achieved by forcing the population to use face masks whenever they interact socially with others. This intervention is easier to implement because every individual has their own responsibility to cut the chain of COVID19 transmission, starting with themselves.
In a similar way, we also can analyze the impact of vaccination to \({\mathcal {R}}_0\). Taking the derivative of \({\mathcal {R}}_0\) respect to \(u_3\) gives
which always negative. Hence, vaccination rate is inversely proportional to \({\mathcal {R}}_0\). From Fig. 2, it can be observed by the red curve that without implementation of a vaccine and social distancing, the basic reproduction number is greater than unity, which indicates a high chance of COVID19 being endemic in the population. Furthermore, we can observe that without vaccination intervention, the transmission rate \(\beta \) must be reduced by greater than \(39\%\) to maintain the basic reproduction number less than unity, and thus provide an opportunity to eradicate COVID19 from the population. With the implementation of the vaccine at a constant rate of 0.001, we can see that the transmission rate must only be reduced by 10%, rather than 39%. This means that it is not necessary to overimplement social distancing; hence, economic and social activities could function more normally. If the vaccination rate is given at a higher rate, which in our experiment we chose 0.002 and 0.003, it can be observed that social distancing is no longer required in that the basic reproduction number decreases to less than unity. Hence, we can conclude that the intervention of vaccination has an excellent potential to allow the government to relax the social distancing intervention and to eradicate COVID19 from the population.
Discussion
Using the bestfir parameter based on incidence data in Jakarta, our proposed model indicates that the control measures of early detection, rapid test and vaccination has a potential to avoid huge size of endemic of COVID19 in the city of Jakarta. Implementation of vaccination strategy in the near future can be used to relaxed social distancing policy such that the social and economy activity in the population can back to normal, and keep the spread of COVID19 as low as possible.
Limitations
Our results in this article provide preliminary results in our effort to understand how far we can rely on a potential COVID19 vaccine, especially in Jakarta. Important questions remain undetermined in this research, and the precise answers must be found as soon as possible. The important questions that should be considered in future research are as follows: 1) what type of population should be considered for the vaccine intervention? This is important because the budget for implementation is frequently limited, and 2) although our result demonstrate a potential positive effect of the vaccine for eradicating COVID19, how far can we rely on this intervention? How high a vaccine efficacy is required to impact the level of success of the COVID19 eradication program? These questions not yet answered on our model.
Availability of data and materials
The data used to support findings of this study is available from the corresponding author upon request.
Abbreviations
 COVID19:

Coronavirus disease 2019
References
Gorbalenya AE, Baker SC, Baric RS, et al. The species severe acute respiratory syndromerelated coronavirus: classifying 2019nCoV and naming it SARSCoV2. Nat Microbiol. 2020;5:536–44.
World Health Organization (WHO). Statement on the second meeting of the international health regulations (2005) emergency committee regarding the outbreak of novel coronavirus (2019nCoV). 2020a. Archived from the original on 31 January 2020. Accessed 30 Jan 2020.
World Health Organization (WHO). WHO DirectorGenerals opening remarks at the media briefing on COVID1911 March 2020. 2020. Accessed 11 Mar 2020.
Covid Coronavirus Pandemic data. https://www.worldometers.info/coronavirus/#countries. Accessed 2 Nov 2020.
Shereen MA, Khan S, Kazmi A, Bashir N, Siddique R. COVID19 infection: origin, transmission, and characteristics of human coronaviruses. J Adv Res. 2020;24:91–8.
Lai CC, Shih TP, Ko WC, Tang HJ, Hsueh PR. Severe acute respiratory syndrome coronavirus 2 (SARSCoV2) and corona virus disease2019 (COVID19): the epidemic and the challenges. Int J Antimicrob Agents. 2020;55(3):105924.
Aldila D. Costeffectiveness and backward bifurcation analysis on covid19 transmission model considering direct and indirect transmission. Commun Math Biol Neurosci. 2020;49(1):28.
Aldila D, Ndii MZ, Samiadji BM. Optimal control on COVID19 eradication program in Indonesia under the effect of community awareness. Math Biosci Eng. 2020;17(6):6355–89.
Aldila D. Analyzing the impact of the media campaign and rapid testing for COVID19 as an optimal control problem in East Java, Indonesia. Chaos Solitons Fractals. 2020;141:110364.
Lai S, Ruktanonchai NW, Zhou L, et al. Effect of nonpharmaceutical interventions to contain COVID19 in China. Nature. 2020;585:410–3.
Lau H, Khosrawipour V, Kocbach P, Mikolajczyk A, Schubert J, Bania J, Khosrawipour T. The positive impact of lockdown in Wuhan on containing the COVID19 outbreak in China. J Travel Med. 2020;27(3):taaa037.
Aldila D, Khoshnaw SH, Safitri E, Anwar YR, Bakry AR, Samiadji BM, Anugerah DA, Gh MF, Ayulani ID, Salim SN. A mathematical study on the spread of COVID19 considering social distancing and rapid assessment: the case of Jakarta, Indonesia. Chaos Solitons Fractals. 2020;139:110042.
Din A, Li Y, Khan T, Zaman G. Mathematical analysis of spread and control of the novel corona virus (COVID19) in China. Chaos Solitons Fractals. 2020;141:110286.
Ndii M, Hadisoemarto P, Agustian D, Supriatna A. An analysis of covid19 transmission in indonesia and saudi arabia. Commun Biomath Sci. 2020;3(1):19–27.
Gumel AB, Iboi EA, Ngonghala C, Elbasha EH. A primer on using mathematics to understand COVID19dynamics: modeling, analysis and simulations. Infect Disease Model. 2021;6:48–168.
Iboi EA, Ngonghala C, Gumel AB. Will an imperfect vaccine curtail the COVID19 pandemic in the U.S.? Infect Disease Model. 2020;5:510–24.
Ferguson NM et al. Impact of nonpharmaceutical interventions (NPIs) to reduce COVID19 mortality and health care demand. Imperial.Ac.Uk. 2020;3–20.
Li R, Pei S, Chen B, Song Y, Zhang T, Yang W, Shaman J. Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARScov2). Science. 2020;368(6940):489–93.
Anderson RM, Heesterbeek H, Klinkenberg D, Hollingsworth TD. How will countrybased mitigation measures influence the course of the COVID19 epidemic? Lancet. 2020;395(10228):931–4.
World Health Organization. Coronavirus disease 2019 (COVID19): situation report, 46. WHO; 2020.
Driessche PV, Watmough J. Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Math Biosci. 2002;180(1–2):29–48.
Acknowledgements
We thank to all reviewers for their valuable comments and suggestions.
Funding
The first author is financially supported by the Ministry of Research, Technology and Higher Education of the Republic of Indonesia (Kemenristek DIKTI) with PUPT research grant scheme, 2021.
Author information
Authors and Affiliations
Contributions
DA contributed in the conceptualization, formal analysis, writing and approving the manuscript, and funding acquisition. BMS and GMS were involved in formal analysis and writing the original draft. SHAK and MS were contributed in visualization, review and editing the manuscript.
Corresponding author
Ethics declarations
Ethics approval and consent to participate
Not applicable
Consent for publish
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
About this article
Cite this article
Aldila, D., Samiadji, B.M., Simorangkir, G.M. et al. Impact of early detection and vaccination strategy in COVID19 eradication program in Jakarta, Indonesia. BMC Res Notes 14, 132 (2021). https://doi.org/10.1186/s13104021055409
Received:
Accepted:
Published:
DOI: https://doi.org/10.1186/s13104021055409
Keywords
 COVID19
 Contact tracing
 Rapid testing
 Vaccination
 Basic reproduction number