Analysis of the COVID19 Pandemic Behaviour Based on the Compartmental SEAIRD and Adaptive SVEAIRD Epidemiologic Models

A significant number of people infected by COVID19 do not get sick immediately but become carriers of the disease. These patients might have a certain incubation period. However, the classical compartmental model, SEIR, was not originally designed for COVID19. We used the simple, commonly used SEIR model to retrospectively analyse the initial pandemic data from Singapore. Here, the SEIR model was combined with the actual published Singapore pandemic data, and the key parameters were determined by maximizing the nonlinear goodness of fit R2 and minimizing the root mean square error. These parameters served for the fast and directional convergence of the parameters of an improved model. To cover the quarantine and asymptomatic variables, the existing SEIR model was extended to an infectious disease model with a greater number of population compartments, and with parameter values that were tuned adaptively by solving the nonlinear dynamics equations over the available pandemic data, as well as referring to previous experience with SARS. The contribution presented in this paper is a new model called the adaptive SEAIRD model;it considers the new characteristics of COVID19 and is therefore applicable to a population including asymptomatic carriers. The predictive value is enhanced by tuning of the optimal parameters, whose values better reflect the current pandemic. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.

Association of epidemiological and clinical features with PCR cycle threshold values of SARS-CoV-2 infection: a cross-sectional study.

The cycle threshold (Ct) in quantitative real-time reverse-transcriptase polymerase chain reaction (qRT-PCR) is inversely correlated to the amount of viral nucleic acid or viral load and can be regarded as an indicator of infectivity. We examined the association of socio-demographic and clinical characteristics of severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) polymerase chain reaction (PCR) positive cases with PCR cycle threshold (Ct) values at the time of diagnosis. SARS-CoV-2 cases reported between 12 October 2020 and 24 January 2021 in Regensburg were analyzed employing bivariate and multivariable methods. We included 3,029 SARS-CoV-2 cases (31% asymptomatic at diagnosis) and analyzed the association of case characteristics with Ct values in 2,606 cases. Among symptomatic patients, cough (38.0%), rhinitis (32.4%), headache (32.0), and fever/chills (29.9%) were the most frequent complaints. Ct values ≤20 were more frequent in symptomatic cases (20.9% vs. 11.3%), whereas Ct values >30 were more common in asymptomatic cases (32.6% vs. 18.0%). Ct values >20 and ≤30 were most common in symptomatic and asymptomatic cases (48.0% vs 40.7%). We observed lower median Ct values of E and N gene in symptomatic cases. In a random forest model, the total number of symptoms, respiratory symptoms, and age were most strongly associated with low Ct values. In conclusion, certain symptoms and age were associated with lower Ct values. Ct values can be used as a pragmatic approach in estimating infectivity at the first notification of a case and, thus, in guiding containment measures.

Modified SEIR epidemic model including asymptomatic and hospitalized cases with correct demographic evolution

The aim of this study is to propose a modified Susceptible-Exposed-Infectious-Removed (SEIR) model that describes the time behaviour of symptomatic, asymptomatic and hospitalized patients in an epidemic, taking into account the effect of the demographic evolution. Unlike most of the recent studies where a constant ratio of new individuals is considered, we consider a more correct assumption that the growth ratio is proportional to the total population, following a Logistic law, as is usual in population growth studies for humans and animals. An exhaustive theoretical study is carried out and the basic reproduction number R0 is computed from the model equations. It is proved that if R0<1 then the disease-free manifold is globally asymptotically stable, that is, the epidemics remits. Global and local stability of the equilibrium points is also studied. Numerical simulations are used to show the agreement between numerical results and theoretical properties. The model is fitted to experimental data corresponding to the pandemic evolution of COVID-19 in the Republic of Cuba, showing a proper behaviour of infected cases which let us think that can provide a correct estimation of asymptomatic cases. In conclusion, the model seems to be an adequate tool for the study and control of infectious diseases.

Asymptomatic and Mild SARS-CoV-2 Infections in a Hungarian Outpatient Cohort in the First Year of the COVID-19 Pandemic.

We aimed to estimate the proportion of the population infected with SARS-CoV-2 in the first year of the pandemic. The study population consisted of outpatient adults with mild or no COVID-19 symptoms and was divided into subpopulations with different levels of exposure. Among the subpopulation without known previous COVID-19 contacts, 4143 patients were investigated. Of the subpopulation with known COVID-19 contacts, 594 patients were investigated. IgG- and IgA-seroprevalence and RT-PCR positivity were determined in context with COVID-19 symptoms. Our results suggested no significant age-related differences between participants for IgG positivity but indicated that COVID-19 symptoms occurred most frequently in people aged between 20 and 29 years. Depending on the study population, 23.4-74.0% PCR-positive people (who were symptomless SARS-CoV-2 carriers at the time of the investigation) were identified. It was also observed that 72.7% of the patients remained seronegative for 30 days or more after their first PCR-positive results. This study hoped to contribute to the scientific understanding of the significance of asymptomatic and mild infections in the long persistence of the pandemic.

The SEIR model incorporating asymptomatic cases, behavioral measures, and lockdowns: Lesson learned from the COVID-19 flow in Sweden.

The Sweden approach is unique in handling the COVID-19 flow, compared to other European countries. While other countries have practiced the full lockdowns, Sweden has practiced the lighter lockdowns or the partial lockdowns as public spaces such as cafes and restaurants are allowed to serve their customers subject to government recommendations. This study aims to develop an SEIR model for Sweden capturing important issues such as the roles of behavioral measures, partial lockdowns, and undocumented cases. The suggested SEIR model is probably the first SEIR model capturing the roles of behavioral measures, partial lockdowns, hospital preparedness, and asymptomatic cases for Sweden. The SEIR model can successfully reproduce similar main observed outputs, namely documented infected cases and documented death cases. This study finds that the effects of partial lockdowns effectively start 52 days after the first confirmed case. Again, behavioral measures and partial lockdowns reduce possible infected cases about 22% and 70% respectively. This study also suggests that the Sweden government should step up to the full lockdowns by conducting public closures so COVID-19 flow can be curtailed significantly. Likewise, owing to airborne transmission, protecting vulnerable people such as senior citizens should be prioritised.

Application of deep learning-based diagnostic systems in screening asymptomatic COVID-19 patients among oversea returnees.

INTRODUCTION: Our study aimed to investigate the performance of deep learning (DL)-based diagnostic systems in alerting against COVID-19, especially among asymptomatic individuals coming from overseas, and to analyze the features of identified asymptomatic patients in detail. METHODOLOGY: DL diagnostic systems were deployed to assist in the screening of COVID-19, including the pneumonia system and pulmonary nodules system. 1,917 overseas returnees who underwent CT examination and rRT-PCR tests were enrolled. DL pneumonia system promptly alerted clinicians to suspected COVID-19 after CT examinations while the performance was evaluated with rRT-PCR results as the reference. The radiological features of asymptomatic COVID-19 cases were described according to the Nomenclature of the Fleischner Society. RESULTS: Fifty-three cases were confirmed as COVID-19 patients by rRT-PCR tests, including 5 asymptomatic cases. DL pneumonia system correctly alerted 50 cases as suspected COVID-19 with a sensitivity of 0.9434 and specificity of 0.9592 (within 2 minutes per case); while the pulmonary nodules system alerted 2 of the 3 missed asymptomatic cases. Additionally, five asymptomatic patients presented different characteristics such as elevated creatine kinase level and prolonged prothrombin time, as well as atypical radiological features. CONCLUSIONS: DL diagnostic systems are promising complementary approaches for prompt screening of imported COVID-19 patients, even the imported asymptomatic cases. Unique clinical and radiological characteristics of asymptomatic cases might be of great value in screening as well. ADVANCES IN KNOWLEDGE: DL-based systems are practical, efficient, and reliable to assist radiologists in screening COVID-19 patients. Differential features of asymptomatic patients might be useful to clinicians in the frontline to differentiate asymptomatic cases.

Effect of Lockdown and Mass Testing for the SARS-CoV-2 Omicron Epidemic on Reducing New Infections in Shenzhen, China.

On 14 March 2022, China's tech hub Shenzhen, a mega-city with more than 18 million inhabitants, imposed a one-week citywide lockdown immediately after it observed a surge in infections. We assessed the effect of this one-week lockdown, coupled with mass testing, on reducing the daily number of new confirmed cases and asymptomatic cases during the Omicron wave, using an interrupted time series analysis approach. Our analysis suggests that the one-week citywide lockdown in Shenzhen was effective at lowering both daily new confirmed cases and asymptomatic cases during the Omicron wave. Early detection ensures timely isolation and treatment of infected patients in designated hospitals, and therefore helps lower the prevalence of confirmed cases and asymptomatic cases. Our findings of the immediate increase in asymptomatic cases after lockdown warrant further verifications in other city epidemic scenarios.

COVID-19 case findings and contact tracing in South German nursing homes.

BACKGROUND: The air borne SARS-CoV-2 poses a high threat to the elderly and people with underlying diseases. COVID-19 spread quickly in South German nursing homes and for this reason called for preventive measures by the German government. The aim of this paper is to showcase the testing strategies implemented by the Public Health Department Reutlingen to control the spread of COVID-19 in local nursing homes and to report the results thereof. METHODS: This study reports COVID-19 outbreaks in nursing homes in Reutlingen County and how they were dealt with through extensive testing, contact tracing, isolation and hygiene inspections. The testing strategy consisted of three phases: In phase 1 only suspected cases, in phase 2 all staff and residents, and in phase 3 all suspected cases and their contacts were tested. RESULTS: Nearly all residents (98%) and staff members (92%) of all nursing homes in Reutlingen County were tested for SARS-COV-2. 25 of 37 nursing homes had COVID-19 cases, 5 had 30-81 cases/home. 62% of the 395 nursing homes cases were residents, but less than half of them exhibited symptoms (41%). The cases uncovered in nursing homes represented 26% of all 1529 cases in Reutlingen County during the time of this study. CONCLUSIONS: Many COVID-19 cases were discovered through extensive testing, allowing for early interventions. The results shed light on the COVID-19 situation in nursing homes and allowed for individually designed preventive measures. The results also lead to a change in the German legislation. The outbreak management methods of the Public Health Department Reutlingen may also be applicable in other countries.

Transmission of Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) from pre and asymptomatic infected individuals: a systematic review.

BACKGROUND: The role of SARS-Cov-2-infected persons who develop symptoms after testing (presymptomatics) or not at all (asymptomatics) in the pandemic spread is unknown. OBJECTIVES: To determine infectiousness and probable contribution of asymptomatic persons (at the time of testing) to pandemic SARS-CoV-2 spread. DATA SOURCES: LitCovid, medRxiv, Google Scholar, and WHO Covid-19 databases (to 31 March 2021) and references in included studies. STUDY ELIGIBILITY CRITERIA: Studies with a proven or hypothesized transmission chain based either on serial PCR cycle threshold readings and/or viral culture and/or gene sequencing, with adequate follow-up. PARTICIPANTS: People exposed to SARS-CoV-2 within 2-14 days to index asymptomatic (at time of observation) infected individuals. INTERVENTIONS: Reliability of symptom and signs was assessed within contemporary knowledge; transmission likelihood was assessed using adapted causality criteria. METHODS: Systematic review. We contacted all included studies' corresponding authors requesting further details. RESULTS: We included 18 studies from a diverse setting with substantial methodological variation (this field lacks standardized methodology). At initial testing, prevalence of asymptomatic cases was 12.5-100%. Of these, 6-100% were later determined to be presymptomatic, this proportion varying according to setting, methods of case ascertainment and population. Nursing/care home facilities reported high rates of presymptomatic: 50-100% (n = 3 studies). Fourteen studies were classified as high risk of, and four studies as at moderate risk of symptom ascertainment bias. High-risk studies may be less likely to distinguish between presymptomatic and asymptomatic cases. Six asymptomatic studies and four presymptomatic studies reported culturing infectious virus; data were too sparse to determine infectiousness duration. Three studies provided evidence of possible and three of probable/likely asymptomatic transmission; five studies provided possible and two probable/likely presymptomatic SARS-CoV-2 transmission. CONCLUSION: High-quality studies provide probable evidence of SARS-CoV-2 transmission from presymptomatic and asymptomatic individuals, with highly variable estimated transmission rates.

SARS-CoV-2 Seroprevalence in Lithuania: Results of National Population Survey.

SUMMARY BACKGROUND: Betacoronavirus SARS-CoV-2 has spread in early 2020 worldwide just in several months. The official statistics are consistently collected, but this is mainly based on symptomatic reports. This study was aimed to estimate the seroprevalence of SARS-CoV-2 infection in Lithuanian population. MATERIALS AND METHODS: Study was conducted during August-September 2020 in 6 municipalities of Lithuania. The sample comprised 3087 adult participants from the general population (mean age 53.7 years, 64% female). SARS-CoV-2 antibodies were assessed using AMP IgM/IgG Rapid Test, other data were based on self-report. Seroprevalence was assessed as a crude estimate and as adjusted by sensitivity-specificity of the test. RESULTS: The crude seroprevalence in the total sample was 1.9%, the adjusted - 1.4%, ranging from 0.8% to 2.4% across municipalities. Among seroprevalent cases, 67.2% had IgG, 29.3% had IgM, and 3.5% had both IgG and IgM. An increased risk for seropositive test was observed among people who reported having had close contacts with SARS-CoV-2 positives (OR=5.49, p<0.001). At the borderline significance were female gender (OR=1.75, p=0.082) and non-smoking status (OR=2.95, p=0.072). Among the seropositive participants, 69.0% reported having had no COVID-19 symptoms since 1 March 2020, while 31.0% reported having had at least one of the symptoms. CONCLUSIONS: The SARS-CoV-2 seroprevalence in Lithuanian sample in August-September 2020 was 1.4%, ranging from 0.8% to 2.4% across municipalities. Given the overall official data, by the end of study (11 September 2020) the total COVID-19 rate in Lithuania was 117.5 per 100,000 population or 0.12%. This suggests more than 10 times higher prevalence of virus across the population than the official estimates.

Estimating the Prevalence of Asymptomatic COVID-19 Cases and Their Contribution in Transmission - Using Henan Province, China, as an Example.

Background: Novel coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-COV-2), is now sweeping across the world. A substantial proportion of infections only lead to mild symptoms or are asymptomatic, but the proportion and infectivity of asymptomatic infections remains unknown. In this paper, we proposed a model to estimate the proportion and infectivity of asymptomatic cases, using COVID-19 in Henan Province, China, as an example. Methods: We extended the conventional susceptible-exposed-infectious-recovered model by including asymptomatic, unconfirmed symptomatic, and quarantined cases. Based on this model, we used daily reported COVID-19 cases from January 21 to February 26, 2020, in Henan Province to estimate the proportion and infectivity of asymptomatic cases, as well as the change of effective reproductive number, R t . Results: The proportion of asymptomatic cases among COVID-19 infected individuals was 42% and the infectivity was 10% that of symptomatic ones. The basic reproductive number R 0 = 2.73, and R t dropped below 1 on January 31 under a series of measures. Conclusion: The spread of the COVID-19 epidemic was rapid in the early stage, with a large number of asymptomatic infected individuals having relatively low infectivity. However, it was quickly brought under control with national measures.

Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study.

BACKGROUND: The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. METHODS: By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. RESULTS: We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. CONCLUSIONS: We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.

Modelling dynamics of coronavirus disease 2019 spread for pandemic forecasting based on Simulink.

In this paper, we demonstrate the application of MATLAB to develop a pandemic prediction system based on Simulink. The susceptible-exposed-asymptomatic but infectious-symptomatic and infectious (severe infected population + mild infected population)-recovered-deceased (SEAI(I1+I2)RD) physical model for unsupervised learning and two types of supervised learning, namely, fuzzy proportional-integral-derivative (PID) and wavelet neural-network PID learning, are used to build a predictive-control system model that enables self-learning artificial intelligence (AI)-based control. After parameter setting, the data entering the model are predicted, and the value of the data set at a future moment is calculated. PID controllers are added to ensure that the system does not diverge at the beginning of iterative learning. To adapt to complex system conditions and afford excellent control, a wavelet neural-network PID control strategy is developed that can be adjusted and corrected in real time, according to the output error.

Lessons from the devastating impact of the first COVID-19 wave in Italy.

Herein, we are critically examining the chain of events and discussing previously unrecognized factors that led to the 'perfect COVID-19 storm' in northern Italy during the first epidemic wave in spring 2020. SARS-CoV-2 was circulating uncontrollably at least for five weeks before the adoption of containment measures, and the role of exponential growth in the spread of the virus, conveyed by a high R0, was likely underestimated. An understanding of this failure's causes and contexts will help us to control the strong second wave of the pandemic we are now facing in Europe, and to be better prepared for future outbreaks.

A new SEAIRD pandemic prediction model with clinical and epidemiological data analysis on COVID-19 outbreak.

Measuring the spread of disease during a pandemic is critically important for accurately and promptly applying various lockdown strategies, so to prevent the collapse of the medical system. The latest pandemic of COVID-19 that hits the world death tolls and economy loss very hard, is more complex and contagious than its precedent diseases. The complexity comes mostly from the emergence of asymptomatic patients and relapse of the recovered patients which were not commonly seen during SARS outbreaks. These new characteristics pertaining to COVID-19 were only discovered lately, adding a level of uncertainty to the traditional SEIR models. The contribution of this paper is that for the COVID-19 epidemic, which is infectious in both the incubation period and the onset period, we use neural networks to learn from the actual data of the epidemic to obtain optimal parameters, thereby establishing a nonlinear, self-adaptive dynamic coefficient infectious disease prediction model. On the basis of prediction, we considered control measures and simulated the effects of different control measures and different strengths of the control measures. The epidemic control is predicted as a continuous change process, and the epidemic development and control are integrated to simulate and forecast. Decision-making departments make optimal choices. The improved model is applied to simulate the COVID-19 epidemic in the United States, and by comparing the prediction results with the traditional SEIR model, SEAIRD model and adaptive SEAIRD model, it is found that the adaptive SEAIRD model's prediction results of the U.S. COVID-19 epidemic data are in good agreement with the actual epidemic curve. For example, from the prediction effect of these 3 different models on accumulative confirmed cases, in terms of goodness of fit, adaptive SEAIRD model (0.99997) ≈ SEAIRD model (0.98548) > Classical SEIR model (0.66837); in terms of error value: adaptive SEAIRD model (198.6563) < < SEAIRD model(4739.8577) < < Classical SEIR model (22,652.796); The objective of this contribution is mainly on extending the current spread prediction model. It incorporates extra compartments accounting for the new features of COVID-19, and fine-tunes the new model with neural network, in a bid of achieving a higher level of prediction accuracy. Based on the SEIR model of disease transmission, an adaptive model called SEAIRD with internal source and isolation intervention is proposed. It simulates the effects of the changing behaviour of the SARS-CoV-2 in U.S. Neural network is applied to achieve a better fit in SEAIRD. Unlike the SEIR model, the adaptive SEAIRD model embraces multi-group dynamics which lead to different evolutionary trends during the epidemic. Through the risk assessment indicators of the adaptive SEAIRD model, it is convenient to measure the severity of the epidemic situation for consideration of different preventive measures. Future scenarios are projected from the trends of various indicators by running the adaptive SEAIRD model.

Suppression of Covid-19 outbreak among healthcare workers at the Treviso Regional Hospital, Italy and lessons for ophthalmologists.

PURPOSE: To describe a strategy to reduce Covid-19 spread among healthcare workers and provide ophthalmologists with recommendations useful for a possible second wave of Covid-19 in Autumn. METHODS: Epidemiological surveillance at the Cà Foncello Hospital (Veneto, Italy) since 24 February 2020 to 24 April 2020 when the municipality of Treviso was hit by the Covid-19 outbreak. The number of naso-pharigeal (NP) swabs performed was 7010. RESULTS: The number of infected among healthcare workers was 209/ 3924 (5.32%): medical doctors: 28 cases / 498 (5.6%). None among ophthalmologists; specialized nurses: 86/1294 (6.4%) None in the ophthalmic unit; intermediate care technicians: 68/463 (14.7%). The 46% of the positive tested were asymptomatic. We share key suggested actions for the reorganization in ophthalmological services: be part of a global epidemiological local strategy of containment (Testing, Tracing, Treating); protect your department: Keep on screening patients by telephone interview before entering the hospital; promote continuous and appropriate use of PPE both for doctors and for patients; make any effort to obtain a continuous flow of patients in every line of the ophthalmic service; treat appropriately any single patient with vision threatening condition; avoid unnecessary or futile testings and examinations. CONCLUSION: The Treviso model shows that it is possible and safe to keep on performing high risk hospital activities like ophthalmology, even in the epicenter of covid outbreak, if adequate actions are performed. We discuss about the value of NP swabs and serological tests as a strategy in case of a second wave of infections.

Changing epidemiology of COVID-19.

Background: We analyzed the epidemiology of COVID-19 in Regensburg after the first wave ended in June 2020 and compared it with patients' characteristics and symptoms in late summer/early autumn 2020. Methods: Retrospective analysis of epidemiological data from Regensburg (city/county) on age and initial symptoms as reported during case investigation for containment. Observed periods: March 7, 2020 to June 6, 2020 and August 12, 2020 to October 9, 2020. Results: The proportion of asymptomatic persons who tested positive for SARS-COV-2 in the second period was 55% (286 of 520 cases), whereas during the first wave from March to June 2020 this percentage was 14.4% (169 of 1,170 cases). A comparison of typical symptoms shows that the most common symptoms of COVID-19 in the first wave (cough, fever and generally feeling ill) were less often reported in the second period: cough 14% vs. 42%, fever 17% vs. 38%, general signs of illness 14% vs. 22% in the second vs. first period, respectively overall cases were younger in the second period, the median age of asymptomatic cases was comparable in both periods. The case fatality rate for the first period was 2.1%, in the second it was 0.2%. Discussion: The epidemiological situation in the second period is different from that during the first wave. We observed a considerable proportion of questionable cases in August/September 2020 (asymptomatic cases, high ct values, often only detection of one gene). False positive cases/non-contagious cases have to be taken into account for this period. On-demand or free-of-charge testing for asymptomatic persons will lower the positive predictive value of tests and place a high burden on finite capacities.

Modelling the spread of SARS-CoV-2 pandemic - Impact of lockdowns & interventions.

BACKGROUND & OBJECTIVES: To handle the current COVID-19 pandemic in India, multiple strategies have been applied and implemented to slow down the virus transmission. These included clinical management of active cases, rapid development of treatment strategies, vaccines computational modelling and statistical tools to name a few. This article presents a mathematical model for a time series prediction and analyzes the impact of the lockdown. METHODS: Several existing mathematical models were not able to account for asymptomatic patients, with limited testing capability at onset and no data on serosurveillance. In this study, a new model was used which was developed on lines of susceptible-asymptomatic-infected-recovered (SAIR) to assess the impact of the lockdown and make predictions on its future course. Four parameters were used, namely ß, γ, η and ε. ß measures the likelihood of the susceptible person getting infected, and γ denotes recovery rate of patients. The ratio ß/γ is denoted by R0 (basic reproduction number). RESULTS: The disease spread was reduced due to initial lockdown. An increase in γ reflects healthcare and hospital services, medications and protocols put in place. In Delhi, the predictions from the model were corroborated with July and September serosurveys, which showed antibodies in 23.5 and 33 per cent population, respectively. INTERPRETATION & CONCLUSIONS: The SAIR model has helped understand the disease better. If the model is correct, we may have reached herd immunity with about 380 million people already infected. However, personal protective measures remain crucial. If there was no lockdown, the number of active infections would have peaked at close to 14.7 million, resulted in more than 2.6 million deaths, and the peak would have arrived by June 2020. The number of deaths with the current trends may be less than 0.2 million.

[Advances on the asymptomatic infection of COVID-19].

The COVID-19 outbreak in China has been gradually controlled. At present, the management and risk assessment of asymptomatic infected cases has become an urgent problem to be addressed. Asymptomatic case is mainly detected by close contact screening, cluster epidemic investigation, infection source tracking investigation, and active detection of target population. Currently, research on the spread risk from asymptomatic cases was limited, and lacking the data relates to the distribution of asymptomatic cases in large community population. Pathogen detection using PCR is suitable for screening in close contacts of confirmed cases and should be started as early as possible. The antibody test is more suitable for screening in general population where the source of infection is unclear. The management of asymptomatic cases now in China focuses on isolation and medical observation according to the guideline of "early detection, early report, early isolation and early treatment" .

A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia.

The aim of this study is to investigate the effects of rapid testing and social distancing in controlling the spread of COVID-19, particularly in the city of Jakarta, Indonesia. We formulate a modified susceptible exposed infectious recovered compartmental model considering asymptomatic individuals. Rapid testing is intended to trace the existence of asymptomatic infected individuals among the population. This asymptomatic class is categorized into two subclasses: detected and undetected asymptomatic individuals. Furthermore, the model considers the limitations of medical resources to treat an infected individual in a hospital. The model shows two types of equilibrium point: COVID-19 free and COVID-19 endemic. The COVID-19-free equilibrium point is locally and asymptotically stable if the basic reproduction number ( R 0 ) is less than unity. In contrast, COVID-19-endemic equilibrium always exists when R 0 > 1 . The model can also show a backward bifurcation at R 0 = 1 whenever the treatment saturation parameter, which describes the hospital capacity, is larger than a specific threshold. To justify the model parameters, we use the incidence data from the city of Jakarta, Indonesia. The data pertain to infected individuals who self-isolate in their homes and visit the hospital for further treatment. Our numerical experiments indicate that strict social distancing has the potential to succeed in reducing and delaying the time of an outbreak. However, if the strict social distancing policy is relaxed, a massive rapid-test intervention should be conducted to avoid a large-scale outbreak in the future.