COVID-19 in South Korea.

A novel coronavirus (severe acute respiratory syndrome-CoV-2) that initially originated from Wuhan, China, in December 2019 has already caused a pandemic. While this novel coronavirus disease (COVID-19) frequently induces mild diseases, it has also generated severe diseases among certain populations, including older-aged individuals with underlying diseases, such as cardiovascular disease and diabetes. As of 31 March 2020, a total of 9786 confirmed cases with COVID-19 have been reported in South Korea. South Korea has the highest diagnostic rate for COVID-19, which has been the major contributor in overcoming this outbreak. We are trying to reduce the reproduction number of COVID-19 to less than one and eventually succeed in controlling this outbreak using methods such as contact tracing, quarantine, testing, isolation, social distancing and school closure. This report aimed to describe the current situation of COVID-19 in South Korea and our response to this outbreak.

Spatial heterogeneity and infection patterns on epidemic transmission disclosed by a combined contact-dependent dynamics and compartmental model.

Epidemics, such as COVID-19, have caused significant harm to human society worldwide. A better understanding of epidemic transmission dynamics can contribute to more efficient prevention and control measures. Compartmental models, which assume homogeneous mixing of the population, have been widely used in the study of epidemic transmission dynamics, while agent-based models rely on a network definition for individuals. In this study, we developed a real-scale contact-dependent dynamic (CDD) model and combined it with the traditional susceptible-exposed-infectious-recovered (SEIR) compartment model. By considering individual random movement and disease spread, our simulations using the CDD-SEIR model reveal that the distribution of agent types in the community exhibits spatial heterogeneity. The estimated basic reproduction number R0 depends on group mobility, increasing logarithmically in strongly heterogeneous cases and saturating in weakly heterogeneous conditions. Notably, R0 is approximately independent of virus virulence when group mobility is low. We also show that transmission through small amounts of long-term contact is possible due to short-term contact patterns. The dependence of R0 on environment and individual movement patterns implies that reduced contact time and vaccination policies can significantly reduce the virus transmission capacity in situations where the virus is highly transmissible (i.e., R0 is relatively large). This work provides new insights into how individual movement patterns affect virus spreading and how to protect people more efficiently.

Epidemiological inference for emerging viruses using segregating sites.

Epidemiological models are commonly fit to case and pathogen sequence data to estimate parameters and to infer unobserved disease dynamics. Here, we present an inference approach based on sequence data that is well suited for model fitting early on during the expansion of a viral lineage. Our approach relies on a trajectory of segregating sites to infer epidemiological parameters within a Sequential Monte Carlo framework. Using simulated data, we first show that our approach accurately recovers key epidemiological quantities under a single-introduction scenario. We then apply our approach to SARS-CoV-2 sequence data from France, estimating a basic reproduction number of approximately 2.3-2.7 under an epidemiological model that allows for multiple introductions. Our approach presented here indicates that inference approaches that rely on simple population genetic summary statistics can be informative of epidemiological parameters and can be used for reconstructing infectious disease dynamics during the early expansion of a viral lineage.

A COVID-19 Infection Model Considering the Factors of Environmental Vectors and Re-Positives and Its Application to Data Fitting in Japan and Italy.

COVID-19, which broke out globally in 2019, is an infectious disease caused by a novel strain of coronavirus, and its spread is highly contagious and concealed. Environmental vectors play an important role in viral infection and transmission, which brings new difficulties and challenges to disease prevention and control. In this paper, a type of differential equation model is constructed according to the spreading functions and characteristics of exposed individuals and environmental vectors during the virus infection process. In the proposed model, five compartments were considered, namely, susceptible individuals, exposed individuals, infected individuals, recovered individuals, and environmental vectors (contaminated with free virus particles). In particular, the re-positive factor was taken into account (i.e., recovered individuals who have lost sufficient immune protection may still return to the exposed class). With the basic reproduction number R0 of the model, the global stability of the disease-free equilibrium and uniform persistence of the model were completely analyzed. Furthermore, sufficient conditions for the global stability of the endemic equilibrium of the model were also given. Finally, the effective predictability of the model was tested by fitting COVID-19 data from Japan and Italy.

Age-dependent final size equation to anticipate mortality impact of COVID-19 in China.

Before reopening society in December 2022, China had not achieved sufficiently high vaccination coverage among people aged 80 years and older, who are vulnerable to severe infection and death owing to COVID-19. Suddenly ending the zero-COVID policy was anticipated to lead to substantial mortality. To investigate the mortality impact of COVID-19, we devised an age-dependent transmission model to derive a final size equation, permitting calculation of the expected cumulative incidence. Using an age-specific contact matrix and published estimates of vaccine effectiveness, final size was computed as a function of the basic reproduction number, R0. We also examined hypothetical scenarios in which third-dose vaccination coverage was increased in advance of the epidemic, and also in which mRNA vaccine was used instead of inactivated vaccines. Without additional vaccination, the final size model indicated that a total of 1.4 million deaths (half of which were among people aged 80 years and older) were anticipated with an assumed R0 of 3.4. A 10% increase in third-dose coverage would prevent 30,948, 24,106, and 16,367 deaths, with an assumed second-dose effectiveness of 0%, 10%, and 20%, respectively. With mRNA vaccine, the mortality impact would have been reduced to 1.1 million deaths. The experience of reopening in China indicates the critical importance of balancing pharmaceutical and non-pharmaceutical interventions. Ensuring sufficiently high vaccination coverage is vital in advance of policy changes.

An age-of-infection model with both symptomatic and asymptomatic infections.

We formulate a general age-of-infection epidemic model with two pathways: the symptomatic infections and the asymptomatic infections. We then calculate the basic reproduction number [Formula: see text] and establish the final size relation. It is shown that the ratio of accumulated counts of symptomatic patients and asymptomatic patients is determined by the symptomatic ratio f which is defined as the probability of eventually becoming symptomatic after being infected. We also formulate and study a general age-of-infection model with disease deaths and with two infection pathways. The final size relation is investigated, and the upper and lower bounds for final epidemic size are given. Several numerical simulations are performed to verify the analytical results.

Spatially explicit effective reproduction numbers from incidence and mobility data.

Current methods for near real-time estimation of effective reproduction numbers from surveillance data overlook mobility fluxes of infectors and susceptible individuals within a spatially connected network (the metapopulation). Exchanges of infections among different communities may thus be misrepresented unless explicitly measured and accounted for in the renewal equations. Here, we first derive the equations that include spatially explicit effective reproduction numbers, ℛk(t), in an arbitrary community k. These equations embed a suitable connection matrix blending mobility among connected communities and mobility-related containment measures. Then, we propose a tool to estimate, in a Bayesian framework involving particle filtering, the values of ℛk(t) maximizing a suitable likelihood function reproducing observed patterns of infections in space and time. We validate our tools against synthetic data and apply them to real COVID-19 epidemiological records in a severely affected and carefully monitored Italian region. Differences arising between connected and disconnected reproduction numbers (the latter being calculated with existing methods, to which our formulation reduces by setting mobility to zero) suggest that current standards may be improved in their estimation of disease transmission over time.

Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation.

HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV/AIDS and COVID-19 co-infection in the community under consideration of the study.

Forward-backward and period doubling bifurcations in a discrete epidemic model with vaccination and limited medical resources.

A discrete epidemic model with vaccination and limited medical resources is proposed to understand its underlying dynamics. The model induces a nonsmooth two dimensional map that exhibits a surprising array of dynamical behavior including the phenomena of the forward-backward bifurcation and period doubling route to chaos with feasible parameters in an invariant region. We demonstrate, among other things, that the model generates the above described phenomena as the transmission rate or the basic reproduction number of the disease gradually increases provided that the immunization rate is low, the vaccine failure rate is high and the medical resources are limited. Finally, the numerical simulations are provided to illustrate our main results.

Correlation of viral loads in disease transmission could affect early estimates of the reproduction number.

Early estimates of the transmission properties of a newly emerged pathogen are critical to an effective public health response, and are often based on limited outbreak data. Here, we use simulations to investigate how correlations between the viral load of cases in transmission chains can affect estimates of these fundamental transmission properties. Our computational model simulates a disease transmission mechanism in which the viral load of the infector at the time of transmission influences the infectiousness of the infectee. These correlations in transmission pairs produce a population-level convergence process during which the distributions of initial viral loads in each subsequent generation converge to a steady state. We find that outbreaks arising from index cases with low initial viral loads give rise to early estimates of transmission properties that could be misleading. These findings demonstrate the potential for transmission mechanisms to affect estimates of the transmission properties of newly emerged viruses in ways that could be operationally significant to a public health response.

Perceptive movement of susceptible individuals with memory.

The perception of susceptible individuals naturally lowers the transmission probability of an infectious disease but has been often ignored. In this paper, we formulate and analyze a diffusive SIS epidemic model with memory-based perceptive movement, where the perceptive movement describes a strategy for susceptible individuals to escape from infections. We prove the global existence and boundedness of a classical solution in an n-dimensional bounded smooth domain. We show the threshold-type dynamics in terms of the basic reproduction number [Formula: see text]: when [Formula: see text], the unique disease-free equilibrium is globally asymptotically stable; when [Formula: see text], there is a unique constant endemic equilibrium, and the model is uniformly persistent. Numerical analysis exhibits that when [Formula: see text], solutions converge to the endemic equilibrium for slow memory-based movement and they converge to a stable periodic solution when memory-based movement is fast. Our results imply that the memory-based movement cannot determine the extinction or persistence of infectious disease, but it can change the persistence manner.

Estimating the time-dependent effective reproduction number and vaccination rate for COVID-19 in the USA and India.

The effective reproduction number, $ R_t $, is a vital epidemic parameter utilized to judge whether an epidemic is shrinking, growing, or holding steady. The main goal of this paper is to estimate the combined $ R_t $ and time-dependent vaccination rate for COVID-19 in the USA and India after the vaccination campaign started. Accounting for the impact of vaccination into a discrete-time stochastic augmented SVEIR (Susceptible-Vaccinated-Exposed-Infectious-Recovered) model, we estimate the time-dependent effective reproduction number $ (R_t) $ and vaccination rate $ (\xi_t) $ for COVID-19 by using a low pass filter and the Extended Kalman Filter (EKF) approach for the period February 15, 2021 to August 22, 2022 in India and December 13, 2020 to August 16, 2022 in the USA. The estimated $ R_t $ and $ \xi_t $ show spikes and serrations with the data. Our forecasting scenario represents the situation by December 31, 2022 that the new daily cases and deaths are decreasing for the USA and India. We also noticed that for the current vaccination rate, $ R_t $ would remain greater than one by December 31, 2022. Our results are beneficial for the policymakers to track the status of the effective reproduction number, whether it is greater or less than one. As restrictions in these countries ease, it is still important to maintain safety and preventive measures.

A numerical study of COVID-19 epidemic model with vaccination and diffusion.

The coronavirus infectious disease (or COVID-19) is a severe respiratory illness. Although the infection incidence decreased significantly, still it remains a major panic for human health and the global economy. The spatial movement of the population from one region to another remains one of the major causes of the spread of the infection. In the literature, most of the COVID-19 models have been constructed with only temporal effects. In this paper, a vaccinated spatio-temporal COVID-19 mathematical model is developed to study the impact of vaccines and other interventions on the disease dynamics in a spatially heterogeneous environment. Initially, some of the basic mathematical properties including existence, uniqueness, positivity, and boundedness of the diffusive vaccinated models are analyzed. The model equilibria and the basic reproductive number are presented. Further, based upon the uniform and non-uniform initial conditions, the spatio-temporal COVID-19 mathematical model is solved numerically using finite difference operator-splitting scheme. Furthermore, detailed simulation results are presented in order to visualize the impact of vaccination and other model key parameters with and without diffusion on the pandemic incidence. The obtained results reveal that the suggested intervention with diffusion has a significant impact on the disease dynamics and its control.

The importance of quarantine: modelling the COVID-19 testing process.

We incorporate the disease state and testing state into the formulation of a COVID-19 epidemic model. For this model, the basic reproduction number is identified and its dependence on model parameters related to the testing process and isolation efficacy is discussed. The relations between the basic reproduction number, the final epidemic and peak sizes, and the model parameters are further explored numerically. We find that fast test reporting does not always benefit the control of the COVID-19 epidemic if good quarantine while awaiting test results is implemented. Moreover, the final epidemic and peak sizes do not always increase along with the basic reproduction number. Under some circumstances, lowering the basic reproduction number increases the final epidemic and peak sizes. Our findings suggest that properly implementing isolation for individuals who are waiting for their testing results would lower the basic reproduction number as well as the final epidemic and peak sizes.

Resurgence of Omicron BA.2 in SARS-CoV-2 infection-naive Hong Kong.

Hong Kong experienced a surge of Omicron BA.2 infections in early 2022, resulting in one of the highest per-capita death rates of COVID-19. The outbreak occurred in a dense population with low immunity towards natural SARS-CoV-2 infection, high vaccine hesitancy in vulnerable populations, comprehensive disease surveillance and the capacity for stringent public health and social measures (PHSMs). By analyzing genome sequences and epidemiological data, we reconstructed the epidemic trajectory of BA.2 wave and found that the initial BA.2 community transmission emerged from cross-infection within hotel quarantine. The rapid implementation of PHSMs suppressed early epidemic growth but the effective reproduction number (Re) increased again during the Spring festival in early February and remained around 1 until early April. Independent estimates of point prevalence and incidence using phylodynamics also showed extensive superspreading at this time, which likely contributed to the rapid expansion of the epidemic. Discordant inferences based on genomic and epidemiological data underscore the need for research to improve near real-time epidemic growth estimates by combining multiple disparate data sources to better inform outbreak response policy.

[Estimation of serial interval and basic reproductive number for imported cases of COVID-19]. / Estimación del intervalo serial y número reproductivo básico para los casos importados de COVID-19.

OBJECTIVE: To estimate the serial interval and the basic reproduction number of COVID-19 between imported cases during the containment phase in Pereira-Colombia, 2020. METHOD: A quantitative study was carried out to determine the transmission dynamics for COVID-19. Field epidemiological data were used, which included 12 laboratory-confirmed cases with RT-PCR for imported SARS-CoV-2 and their corresponding confirmed secondary cases, including family and social contacts. RESULTS: The serial intervals in COVID-19 fit a Gamma distribution, with a mean of the serial interval of 3.8 days (2.7) and an R0 of 1.7 (95% CI 1.06-2.7) lower than that found in other populations with onset of the outbreak. CONCLUSIONS: A serial interval lower than the incubation period such as that estimated in this study, suggests a presymptomatic transmission period that according to other investigations reaches an average peak at 3.8 days, suggesting that during the field epidemiological investigation the search for contacts Narrowing is performed from at least 2 days before the onset of symptoms of the initial case.

Estimation and sensitivity analysis of a COVID-19 model considering the use of face mask and vaccination.

To model the COVID-19 infection and develop effective control measures, this paper proposes an SEIR-type epidemic model considering the impact of face-mask wearing and vaccination. Firstly, the effective reproduction number and the threshold conditions are obtained. Secondly, based on the data of South Korea from January 20, 2022 to March 21, 2022, the model parameters are estimated. Finally, a sensitivity analysis and the numerical study are conducted. The results show that the face-mask wearing is associated with [Formula: see text] and [Formula: see text] reductions in the numbers of cumulative cases and newly confirmed cases, respectively, after a period of 60 days, when the face mask wearing rate increases by [Formula: see text]. Furthermore, the vaccination rate is associated with [Formula: see text] and [Formula: see text] reductions in the numbers of cumulative cases and the newly confirmed cases, respectively, after the same period of 60 days when the vaccination rate is increased by [Formula: see text]. A combined measure involving face-mask wearing and vaccination may be more effective and reasonable in preventing and controlling this infection. It is also suggested that disease control departments should strongly recommended the wearing of face masks s as well as vaccination to prevent the unvaccinated people from becoming infected.

Quantifying Uncertainty in Mechanistic Models of Infectious Disease.

This primer describes the statistical uncertainty in mechanistic models and provides R code to quantify it. We begin with an overview of mechanistic models for infectious disease, and then describe the sources of statistical uncertainty in the context of a case study on severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). We describe the statistical uncertainty as belonging to 3 categories: data uncertainty, stochastic uncertainty, and structural uncertainty. We demonstrate how to account for each of these via statistical uncertainty measures and sensitivity analyses broadly, as well as in a specific case study on estimating the basic reproductive number, ${R}_0$, for SARS-CoV-2.

Time-variant reproductive number of COVID-19 in Seoul, Korea.

OBJECTIVES: To estimate time-variant reproductive number (Rt) of coronavirus disease 19 based on either number of daily confirmed cases or their onset date to monitor effectiveness of quarantine policies. METHODS: Using number of daily confirmed cases from January 23, 2020 to March 22, 2020 and their symptom onset date from the official website of the Seoul Metropolitan Government and the district office, we calculated Rt using program R's package "EpiEstim". For asymptomatic cases, their symptom onset date was considered as -2, -1, 0, +1, and +2 days of confirmed date. RESULTS: Based on the information of 313 confirmed cases, the epidemic curve was shaped like 'propagated epidemic curve'. The daily Rt based on Rt_c peaked to 2.6 on February 20, 2020, then showed decreased trend and became <1.0 from March 3, 2020. Comparing both Rt from Rt_c and from the number of daily onset cases, we found that the pattern of changes was similar, although the variation of Rt was greater when using Rt_c. When we changed assumed onset date for asymptotic cases (-2 days to +2 days of the confirmed date), the results were comparable. CONCLUSIONS: Rt can be estimated based on Rt_c which is available from daily report of the Korea Centers for Disease Control and Prevention. Estimation of Rt would be useful to continuously monitor the effectiveness of the quarantine policy at the city and province levels.