• Journal of Korean Society for Quality Management
• /
• v.48 no.3
• /
• pp.493-510
• /
• 2020

Purpose: As of July 31, there were 14,336 confirmed cases of COVID-19 in South Korea, including 301 deaths. Since the daily confirmed number of cases hit 909 on February 29, the spread of the disease had gradually decreased due to the active implementation of preventive control interventions, and the daily confirmed number had finally recorded a single digit on April 19. Since May, however, the disease has re-emerged and retaining after June. In order to eradicate the disease, it is necessary to suggest suitable forward preventive strategies by predicting future infectivity of the disease based on the cases so far. Therefore, in this study, we aim to evaluate the transmission potential of the disease in early phases by estimating basic reproduction number and assess the preventive control measures through effective reproduction number. Methods: We used publicly available cases and deaths data regarding COVID-19 in South Korea as of July 31. Using ensemble model integrated stochastic linear birth model and deterministic linear growth model, the basic reproduction number and the effective reproduction number were estimated. Results: Estimated basic reproduction number is 3.1 (95% CI: 3.0-3.2). Effective reproduction number was the highest with 7 on February 15, decreased as of April 20. Since then, the value is gradually increased to more than unity. Conclusion: Preventive policy such as wearing a mask and physical distancing campaigns in the early phase of the outbreak was fairly implemented. However, the infection potential increased due to weakening government policy on May 6. Our results suggest that it seems necessary to implement a stronger policy than the current level.

• Journal of Preventive Medicine and Public Health
• /
• v.53 no.6
• /
• pp.405-408
• /
• 2020

In epidemiology, the basic reproduction number (R₀) is a term that describes the expected number of infections generated by 1 case in a susceptible population. At the beginning of the coronavirus disease 2019 (COVID-19) pandemic, R₀ was frequently referenced by the public health community and the wider public. However, this metric is often misused or misinterpreted. Moreover, the complexity of the process of estimating R₀ has caused difficulties for a substantial number of researchers. In this article, in order to increase the accessibility of this concept, we address several misconceptions related to the threshold characteristics of R₀ and the effective reproduction number (R_t). Moreover, the appropriate interpretation of the metrics is discussed. R₀ should be considered as a population-averaged value that pools the contact structure according to a stochastic transmission process. Furthermore, it is necessary to understand the unavoidable time lag for R_t due to the incubation period of the disease.

• Journal of Preventive Medicine and Public Health
• /
• v.53 no.3
• /
• pp.151-157
• /
• 2020

Objectives: The outbreak of coronavirus disease 2019 (COVID-19) is one of the main public health challenges currently facing the world. Because of its high transmissibility, COVID-19 has already caused extensive morbidity and mortality in many countries throughout the world. An accurate estimation of the basic reproduction number (R₀) of COVID-19 would be beneficial for prevention programs. In light of discrepancies in original research on this issue, this systematic review and meta-analysis aimed to estimate the pooled R₀ for COVID-19 in the current outbreak. Methods: International databases (including Google Scholar, Science Direct, PubMed, and Scopus) were searched to identify studies conducted regarding the R₀ of COVID-19. Articles were searched using the following keywords: "COVID-19" and "basic reproduction number" or "R₀." The heterogeneity among studies was assessed using the I² index, the Cochran Q test, and T². A random-effects model was used to estimate R₀ in this study. Results: The mean reported R₀ in the identified articles was 3.38±1.40, with a range of 1.90 to 6.49. According to the results of the random-effects model, the pooled R₀ for COVID-19 was estimated as 3.32 (95% confidence interval, 2.81 to 3.82). According to the results of the meta-regression analysis, the type of model used to estimate R₀ did not have a significant effect on heterogeneity among studies (p=0.81). Conclusions: Considering the estimated R₀ for COVID-19, reducing the number of contacts within the population is a necessary step to control the epidemic. The estimated overall R₀ was higher than the World Health Organization estimate.

• Journal of applied mathematics & informatics
• /
• v.31 no.5_6
• /
• pp.747-767
• /
• 2013

In this paper we have constructed a mathematical model of alcohol abuse which consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined and sensitivity analysis of $R_0$ indicates that ${\beta}1$ (the transmission coefficient from moderate and occasional drinker to heavy drinker) is the most useful parameter for preventing drinking habit. Stability analysis of the model is made using the basic reproduction number. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0<1$. It is found that, when $R_0=1$, a backward bifurcation can occur and when $R_0>1$, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE under some conditions. Our important analytical findings are illustrated through computer simulation. Epidemiological implications of our analytical findings are addressed critically.

• Journal of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.987-997
• /
• 2017

A deterministic model for the spread of pine wilt disease with asymptomatic carrier trees in the host pine population is designed and rigorously analyzed. We have taken four different classes for the trees, namely susceptible, exposed, asymptomatic carrier and infected, and two different classes for the vector population, namely susceptible and infected. A complete global analysis of the model is given, which reveals that the global dynamics of the disease is completely determined by the associated basic reproduction number, denoted by $\mathcal{R}_0$. If $\mathcal{R}_0$ is less than one, the disease-free equilibrium is globally asymptotically stable, and in such a case, the endemic equilibrium does not exist. If $\mathcal{R}_0$ is greater than one, the disease persists and the unique endemic equilibrium is globally asymptotically stable.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.4
• /
• pp.275-284
• /
• 2010

Deliberate self-harm (DSH) is the act of deliberately harming your own body, such as cutting or burning yourself, without suicidal intent. It has especially become a problem among adolescents and college-age students in institutional settings such as boarding schools, Greek houses, detention centers and hospitals. We focus on contagion of DSH among adolescents and young adults by creating a deterministic epidemiological model. We study the impact of actual peer pressure, virtual peer pressure (the Internet) and treatment analytically in terms of a basic reproduction number through stability analysis of a system of ordinary differential equations. All parameters are approximated and results are also explored by simulations. The model shows that DSH is present in an endemic state in the population considered, and the control strategies are discussed.

• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.685-699
• /
• 2019

This research is focused on a continuous epidemic model of transmission of Plasmodium vivax malaria with a time delay. The model is represented as a system of ordinary differential equations with delay. There are two equilibria, which are the disease-free state and the endemic equilibrium, depending on the basic reproduction number, $R_0$, which is calculated and decreases with the time delay. Moreover, the disease-free equilibrium is locally asymptotically stable if $R_0<1$. If $R_0>1$, a unique endemic steady state exists and is locally stable. Furthermore, Hopf bifurcation is applied to determine the conditions for periodic solutions.

• Journal of applied mathematics & informatics
• /
• v.41 no.1
• /
• pp.107-121
• /
• 2023

An epidemic infectious disease model consists of six compartments viz. Susceptible, Exposed, Infected, Quarantine, Recovered, and Virus with nonlinear saturation incidence rate is proposed to know the viral disease dynamics. There exist two biological equilibrium points for the model system. The system's local and global stability is done through Lyapunov's direct method about equilibrium points. The sensitivity analysis has been performed for the basic reproduction number and equilibrium points through the normalized forward sensitivity index. Sensitivity analysis shows that virus growth and quarantine rates are more sensitive parameters. In support of mathematical conclusions, numerical experimentation has been shown.

• The Pure and Applied Mathematics
• /
• v.30 no.2
• /
• pp.203-220
• /
• 2023

A new modification of the SIS epidemic model incorporating the adaptive host behavior is proposed. Unlike the common situation in most epidemic models, this system has two disease-free equilibrium points, and we were able to prove that as the basic reproduction number approaches the threshold of 1, these two points merge and a Bogdanov-Takens bifurcation of codimension three occurs. The occurrence of this bifurcation is a sign of the complexity of the dynamics of the system near the value 1 of basic reproduction number. Both local and global stability of disease-free and endemic equilibrium point are studied.

• Journal of Veterinary Science
• /
• v.22 no.5
• /
• pp.71.1-71.12
• /
• 2021

Background: African swine fever (ASF) is a hemorrhagic fever occurring in wild boars (Sus scrofa) and domestic pigs. The epidemic situation of ASF in South Korean wild boars has increased the risk of ASF in domestic pig farms. Although basic reproduction number (R₀) can be applied for control policies, it is challenging to estimate the R₀ for ASF in wild boars due to surveillance bias, lack of wild boar population data, and the effect of ASF-positive wild boar carcass on disease dynamics. Objectives: This study was undertaken to estimate the R₀ of ASF in wild boars in South Korea, and subsequently analyze the spatiotemporal heterogeneity. Methods: We detected the local transmission clusters using the spatiotemporal clustering algorithm, which was modified to incorporate the effect of ASF-positive wild boar carcass. With the assumption of exponential growth, R₀ was estimated for each cluster. The temporal change of the estimates and its association with the habitat suitability of wild boar were analyzed. Results: Totally, 22 local transmission clusters were detected, showing seasonal patterns occurring in winter and spring. Mean value of R₀ of each cluster was 1.54. The estimates showed a temporal increasing trend and positive association with habitat suitability of wild boar. Conclusions: The disease dynamics among wild boars seems to have worsened over time. Thus, in areas with a high elevation and suitable for wild boars, practical methods need to be contrived to ratify the control policies for wild boars.