The Value-Based Price for a Bivalent COVID-19 Booster Vaccine in the United Kingdom

Objectives: The United Kingdom (UK) implemented an autumn 2022 booster programme that allowed those at higher risk from COVID-19, including those >= 50 years, to receive a booster to increase protection against infection and subsequent severe outcomes. As the UK transitions out of the pandemic, future booster campaigns may be required to maintain protection against such outcomes. The objective of this analysis was to estimate the value-based price (VBP) for a bivalent COVID-19 vaccine used in a future autumn 2023 campaign in the UK to protect people aged >= 50 years. Method(s): A Susceptible-Exposed-Infected-Recovered (SEIR) model was used to predict infections across a 1-year time horizon starting September 2023 with and without an autumn booster campaign. Initial effectiveness was predicted to be 89% and 97% against infection and hospitalization respectively based on BA.4/BA.5 antibody titers and correlates of protection. A monthly decline in protection of 1.4% and 4.8%, respectively, was assumed based on monovalent vaccine data. A decision tree was used to predict the quality-adjusted life-years (QALY) lost and costs associated with infections. Result(s): Considering a willingness-to-pay (WTP) threshold of 20,000/QALY, the VBP associated with an autumn 2023 booster campaign is 343/dose. Considering a WTP threshold of 30,000, the VBP increases to 476. In sensitivity analyses, excluding the post-infection costs (e.g., long COVID), reduces the VBP by 11%. Varying the hospitalization rates by +/-25% changes the VBP by +/- 6%. Varying hospitalization unit costs only impacts the VBP by 1%. Doubling the rate of waning for booster effectiveness increases the VBP by 54% because the effectiveness provided from past campaigns falls faster and an autumn 2023 booster becomes more valuable. Conclusion(s): While the trajectory of COVID-19 incidence is highly uncertain, pricing the bivalent booster lower than the VBP is expected to result in a cost-effective strategy for the UK.Copyright © 2023

Retrospective Assessment of the Accuracy of Mpox Case Projections in New York City

Background: In mid-2022, New York City (NYC) became the epicenter of the US mpox epidemic. Health authorities were in need of forecasts to anticipate the timing and magnitude of the outbreak. We provided mathematical modelbased projections with methodologies that evolved alongside the epidemic. Here, we retrospectively evaluate our mpox case projections and reflect on potential reasons for accuracies and inaccuracies. Method(s): Early in the outbreak (July 1 - 15, 2022), when the size of the at-risk population was unknown, we performed short-term (2-week) forecasting using exponential regression. Once epidemic growth was no longer exponential (July 15 - Aug. 9), we consulted with the NYC Department of Health and Mental Hygiene regarding populations most-at-risk of mpox based on available epidemiological data. Modelers and epidemiologists collaboratively developed an estimate of 70,180 people at risk, informed by estimates of LGBTQ adults with male sex at birth who had 2+ partners in the last 3 months. We combined this with NYC case count data, NYC vaccination data, and global mpox natural history data to develop a Susceptible-Exposed-Infected-Recovered (SEIR) model, taking into account immunity accrued through vaccination and prior exposure, for longer-term forecasting. Result(s): Initial exponential forecasts of the NYC mpox outbreak were only accurate for very short-term predictions (< 2 weeks) (Figure, top panel). Forecasts were more accurate after 1 week (mean absolute error: 83.0 cases/ wk) than after 2 weeks (mean absolute error: 351.4 cases/wk). In contrast, the SEIR model accurately predicted the decline in cases through the end of Sept. 2022, when cases fell to < 70/wk. Over the period from Aug. 10 to Sept. 24 2022, the mean absolute error of the SEIR-based projection was 8.2 cases per week (Figure, bottom panel). Conclusion(s): Model-based NYC mpox projections provided only short-term accuracy in the early epidemic, but long-term accuracy once the epidemic exited exponential growth and an SEIR model was developed. Cumulative cases and vaccinations when exiting exponential growth, and the epidemiology of those most-at-risk, provided evidence for the likely size of the most-at-risk population - a crucial input for an accurate SEIR model. The ability of the SEIR model to accurately forecast mpox cases was in part attributable to lack of vaccine or immune escape by mpox, in contrast to more rapidly-evolving viruses such as SARS-CoV-2.

Modelling the third wave of the COVID-19 pandemic in Malaysia

Introduction: The COVID-19 pandemic has spread rapidly across the globe and negatively affected healthcare systems worldwide. The objective of this study was to develop Susceptible-Exposed-Infected-Recovered (SEIR) models to forecast daily COVID-19 cases during the third wave in Malaysia. Material(s) and Method(s): SEIR models were developed using the R programming software ODIN interface which were fitted into the Malaysian daily COVID-19 case numbers from 1 April 2021 to 14 July 2021, allowing for the approximation of parameters consisting of incubation period (I), removal rate (L) and disease transmissibility (R). Effects of vaccination was accounted by determining the time varying function for the vaccination rates based on two scenarios;achieve 80% population fully vaccinated by (a) 31 October 2021 and (b) 31 December 2021. Weighted vaccine efficacy was set at 70%. Subsequently forecasts of daily COVID-19 cases based on scenarios (a) and (b) were provided from 15 July 2021 to 31 December 2021. Result(s) and Conclusion(s): Our model calibration estimated that (I), (L), and (R) were 5.2 days, 0.25, and 1.2, respectively. A polynomial (y=20.452x2 - 2E + 06x + 4E +10) and Logarithm (y=-58000ln(x) + 327680) equations was determine to account for the vaccination rates. Scenarios (a) and (b) forecasted that the outbreak would peak on 25 August 2021 with 23,590 cases and 15 September 2021 with 27,051 cases respectively, and subsequently showed a reducing case trend till 31 December 2021. As of 31 December 2021, the highest daily case observed was on 26 August 2021 with 24,599 cases which was very close to the model estimation. The observed cases closely mirrored the down going trend forecasted in scenario (a) until 26 October 2021. Trend of observed cases from November to December 2021 was well within the model forecast range of scenario (a) and (b). SEIR models developed accounting for the effects of vaccination were able to provide reasonable forecasts of daily case trend during the third wave of COVID-19 in Malaysia.

How Modelling and Analytics Informed the South African Government's COVID-19 Planning and Budgeting

Introduction/ Background: The South African COVID-19 Modelling Consortium (SACMC) was established in March 2020 to support government planning and budgeting for COVID-19 related healthcare. We developed tools in response to changing decision maker needs in different stages of the epidemic, allowing the South African government to plan several months ahead of time. Methods: Our tools included generalised SEIR models, shortterm forecasts, cost and budget impact models, and online dashboards to help government and the public visualise our projections during the first wave and track the epidemic trajectory and forecast hospitalisation trends during the second and third wave. Given the rapidly changing nature of the pandemic, the model projections and methods were updated regularly. Projections, forecasts and monitoring metrics were regularly disseminated via dashboards. Results: The updates reflected 1) the changing policy priorities;2) the availability of new data, in particular from South African data systems whose coverage was improving continuously;and 3) the evolving response to COVID-19 in South Africa such as changes in lockdown levels and resulting mobility and contact rates, testing policy, contact tracing strategy, and hospitalisation criteria. Insights into population behaviour, for example in reaction to increases in cases and deaths during first wave in May to August 2020, required the incorporation of behavioural response. Impact: We incorporated these aspects into projecting a third wave and developed additional methodology that allowed us to forecast short-term trends in hospital admissions as the third wave started rolling. The SACMC has further updated the models to incorporate the impact of the vaccines and advise on booster options. Conclusion: The SACMC's models, developed rapidly in an emergency setting and regularly updated with local data, supported national and provincial government to plan several months ahead of time, expand hospital capacity, allocate budgets, and procure additional resources where possible.

COVID-19 Data-Driven SIR Models, October 2021

Introduction/ Background: COVID-19 was declared a global pandemic on March 11, 2020 by the World Health Organization. The Susceptible-Infected-Recovered (SIR) model was used in a bid to predict COVID-19. In this study, we use a data-driven SIR model to simulate the epidemic in Rwanda from March 16, 2020 to October 14, 2021. Methods: The online access of some COVID-19 data to the public has facilitated this research. The study uses publicly available data from Our World In Data (OWID). The COVID-19 reported cases are used to estimate the spreading and the recovery rates. These data-driven parameters are then recast into the basic SIR models and its simple extension, the Susceptible-Exposed-Infected-Recovered (SEIR) model. The Susceptible-Infected-Recovered (SIR) model is one of the most extensively used approaches for modeling infectious diseases. Results: The data-driven SIR model captures a single wave and single variant in some countries but has severe limitations in estimating the end of a wave or the risk of death. However, the SEIR model captures the different waves that were identified in the country but cannot be used to assess the risk of death. Also, the predictive capabilities of the SEIR model yielded better results compared with the SIR model. Impact: The aim of this research is to demonstrate the inadequacy of the SIR model and its extension due to its limitations to estimate waves as well as the mortality risks. Conclusion: The public data has limitations in terms of recovered cases and exposed cases. The limitations identified for the SIR and SEIR models, which consist of not being able to estimate a wave or the risk of death, suggest the use of improved mathematical approaches to predict the outbreak of COVID-19.

Research on Epidemic Spreading Model Based on Double Groups

In recent years, Corona Virus Disease 2019 (COVID-19), as a highly contagious disease worldwide, poses a serious threat to public health. It is necessary to scientifically predict the development of the epidemic and to study and judge the situation of the epidemic. Based on the Susceptible-Exposed-Infectious-Recovered (SEIR) model, this paper divides the population according to infectivity and considers the impact of double groups on the spread of the new coronavirus COVID-19. In the propagation model, important factors such as the incubation period, average healing days, and recovery rate are introduced, and its stability is analyzed and simulated. In the end, the experimental results prove that the model is stable and can achieve the desired expected effect. The research results provide a theoretical basis for the accurate simulation of the spread of the epidemic in the population, and have important research value and practical significance for improving the prevention and control strategy of the epidemic. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Estimating the Impact of School Classroom Sizes on the Probability of Severe Acute Respiratory Syndrome Coronavirus-2 Infectivity or Exposure

Background. Despite schools reopening across the United States in communities with low and high Coronavirus disease 2019 (COVID-19) prevalence, data remain scarce about the effect of classroom size on the transmission of severe acute respiratory syndrome coronavirus-2 (SARS-COV-2) within schools. This study estimates the effect of classroom size on the risk of COVID-19 infection in a closed classroom cohort for varying age groups locally in Durham, North Carolina. Total number of Coronavirus Disease 2019 (COVID-19) infections over a 28-day follow-up period for varying classroom reproduction number (R0) and varying classroom cohort sizes of 15 students, 30 students and 100 students in Durham County, North Carolina. Methods. Using publicly available population and COVID-19 case count data from Durham County, we calculated a weekly average number of new confirmed COVID-19 cases per week between May 3, 2020 and August 22, 2020 according to age categories: < 5 years, 5-9 years, 10-14 years, and 15-19 years. We collated average classroom cohort sizes and enrollment data for each age group by grade level of education for the first month of the 2019-2020 academic school year. Then, using a SEIR compartmental model, we calculated the number of susceptible (S), exposed (E), infectious (I) and recovered (R) students in a cohort size of 15, 30 and 100 students, modelling for classroom reproduction number (R0) of 0.5, 1.5 and 2.5 within a closed classroom cohort over a 14-day and 28-day follow-up period using age group-specific COVID-19 prevalence rates. Results. The SEIR model estimated that the increase in cohort size resulted in up to 5 new COVID-19 infections per 10,000 students whereas the classroom R0 had a stronger effect, with up to 88 new infections per 10,000 students in a closed classroom cohort over time. When comparing different follow-up periods in a closed cohort with R0 of 0.5, we estimated 12 more infected students per 10,000 students over 28 days as compared to 14 days irrespective of cohort size. With a R0 of 2.5, there were 49 more infected students per 10,000 students over 28 days as compared to 14 days. Conclusion. Classroom R0 had a stronger impact in reducing school-based COVID-19 transmission events as compared to cohort size. Additionally, earlier isolation of newly infected students in a closed cohort resulted in fewer new COVID-19 infections within that group. Mitigation strategies should target promoting safe practices within the school setting including early quarantine of newly identified contacts and minimizing COVID-19 community prevalence.

A year into the pandemic: A mathematical model and study of covid-19 in india

COVID-19 has been declared as a global pandemic by the World Health Organization (WHO) since its outbreak in December 2019. In India, as of May 12th 2021, the total number of coronavirus cases and associated deaths are 2,35,57,676 and 2,56,617 respectively. To control the spread of the virus effectively, social distancing, self-isolation and quarantine, lockdowns and mass inoculation are vital. In this paper we propose a deterministic epidemic model which is an extension of the SEIR model to understand the disease dynamics.The proposed model has eight compartments, Susceptible1, Susceptible2, Exposed, Infected, Quarantined, Isolated, Recovered and Dead and is termed as the S1S2EIQJRD model. The basic reproduction number Ris derived for the proposed model and it is shown that for the disease dies out and for the disease is endemic. Numerical simulations for the growth of the virus across India through the span of the outbreak are obtained. The simulation is done on real data and the results obtained may be used to make suitable inferences about the dynamics of the disease and appropriate measures can be taken to control its spread.

Containing the spread of mumps on college campuses.

College campuses are vulnerable to infectious disease outbreaks, and there is an urgent need to develop better strategies to mitigate their size and duration, particularly as educational institutions around the world adapt to in-person instruction during the COVID-19 pandemic. Towards addressing this need, we applied a stochastic compartmental model to quantify the impact of university-level responses to contain a mumps outbreak at Harvard University in 2016. We used our model to determine which containment interventions were most effective and study alternative scenarios without and with earlier interventions. This model allows for stochastic variation in small populations, missing or unobserved case data and changes in disease transmission rates post-intervention. The results suggest that control measures implemented by the University's Health Services, including rapid isolation of suspected cases, were very effective at containing the outbreak. Without those measures, the outbreak could have been four times larger. More generally, we conclude that universities should apply (i) diagnostic protocols that address false negatives from molecular tests and (ii) strict quarantine policies to contain the spread of easily transmissible infectious diseases such as mumps among their students. This modelling approach could be applied to data from other outbreaks in college campuses and similar small population settings.

Predicting COVID-19 epidemiological trend by applying population mobility data in two-stage modeling.

:To predict the epidemiological trend of coronavirus disease 2019 (COVID-19) by mathematical modeling based on the population mobility and the epidemic prevention and control measures. : As of February 8，2020，the information of 151 confirmed cases in Yueqing，Zhejiang province were obtained，including patients' infection process，population mobility between Yueqing and Wuhan，etc. To simulate and predict the development trend of COVID-19 in Yueqing, the study established two-stage mathematical models，integrating the population mobility data with the date of symptom appearance of confirmed cases and the transmission dynamics of imported and local cases. : It was found that in the early stage of the pandemic，the number of daily imported cases from Wuhan (using the date of symptom appearance) was positively associated with the number of population travelling from Wuhan to Yueqing on the same day and 6 and 9 days before that. The study predicted that the final outbreak size in Yueqing would be 170 according to the number of imported cases estimated by consulting the population number travelling from Wuhan to Yueqing and the susceptible-exposed-infectious-recovered (SEIR) model; while the number would be 165 if using the reported daily number of imported cases. These estimates were close to the 170，the actual monitoring number of cases in Yueqing as of April 27，2020. : The two-stage modeling approach used in this study can accurately predict COVID-19 epidemiological trend.

Exploring early prevention and control of COVID-19 outbreak based on system dynamics model analysis.

To explore early prevention and control of coronavirus disease 2019 （COVID-19） outbreak based on system dynamics model analysis. The data of early outbreak of COVID-19 were collected from the World Health Organization，covering countries of the China，United States，United Kingdom，Australia，Serbia and Italy. The susceptible-exposed-infected-recovered （SEIR） model was generalized and then its parameters were optimized. According to the parameters in the basic infection number expression，the sensitivity in the system dynamics model was used to quantitatively analyze the influence of the protection rate，infection rate and average quarantine time on the early spread of the outbreak. Based on the analysis results，targeted prevention and control measures for the early outbreak of COVID-19 were proposed. The generalized SEIR model had a good fit for the early prediction and evaluation of COVID-19 outbreaks in six countries. The spread of COVID-19 was mainly affected by the protection rate，infection rate and average quarantine time. The improvement of the protection rate in the first ays was the most important:the greater the protection rate，the fewer the number of confirmed cases. The infection rate in the first 5 days was the most critical:the smaller the infection rate，the fewer the number of confirmed cases. The average quarantine time in the first 5 days was very important:the shorter the average quarantine time，the fewer the number of confirmed cases. Through the comparison of key parameters of six countries，Australia and China had implemented strict epidemic prevention policies，which had resulted in good epidemic prevention effects. In the early stage of the outbreak，it is necessary to improve the protection rate，shorten the average quarantine time，and implement strict isolation policies to curb the spread of COVID-19.

Impact of Wuhan lockdown on the spread of COVID-19 in China: a study based on the data of population mobility.

This study aimed to quantitatively assess the effectiveness of the Wuhan lockdown measure on controlling the spread of coronavirus diesase 2019 (COVID-19). : Firstly，estimate the daily new infection rate in Wuhan before January 23，2020 when the city went into lockdown by consulting the data of Wuhan population mobility and the number of cases imported from Wuhan in 217 cities of Mainland China. Then estimate what the daily new infection rate would have been in Wuhan from January 24 to January 30th if the lockdown measure had been delayed for 7 days，assuming that the daily new infection in Wuhan after January 23 increased in a high，moderate and low trend respectively (using exponential, linear and logarithm growth models). Based on that，calculate the number of infection cases imported from Wuhan during this period. Finally，predict the possible impact of 7-day delayed lockdown in Wuhan on the epidemic situation in China using the susceptible-exposed-infectious-removed (SEIR) model. : The daily new infection rate in Wuhan was estimated to be 0.021%，0.026%，0.029%，0.033% and 0.070% respectively from January 19 to January 23. And there were at least 20 066 infection cases in Wuhan by January 23，2020. If Wuhan lockdown measure had been delayed for 7 days，the daily new infection rate on January 30 would have been 0.335% in the exponential growth model，0.129% in the linear growth model，and 0.070% in the logarithm growth model. Correspondingly，there would have been 32 075，24 819 and 20 334 infection cases travelling from Wuhan to other areas of Mainland China，and the number of cumulative confirmed cases as of March 19 in Mainland China would have been 3.3-3.9 times of the officially reported number. Conclusions: Timely taking city-level lockdown measure in Wuhan in the early stage of COVID-19 outbreak is essential in containing the spread of the disease in China.

Simulating a Community Mental Health Service During the COVID-19 Pandemic: Effects of Clinician-Clinician Encounters, Clinician-Patient-Family Encounters, Symptom-Triggered Protective Behaviour, and Household Clustering.

Objectives: Face-to-face healthcare, including psychiatric provision, must continue despite reduced interpersonal contact during the COVID-19 (SARS-CoV-2 coronavirus) pandemic. Community-based services might use domiciliary visits, consultations in healthcare settings, or remote consultations. Services might also alter direct contact between clinicians. We examined the effects of appointment types and clinician-clinician encounters upon infection rates. Design: Computer simulation. Methods: We modelled a COVID-19-like disease in a hypothetical community healthcare team, their patients, and patients' household contacts (family). In one condition, clinicians met patients and briefly met family (e.g., home visit or collateral history). In another, patients attended alone (e.g., clinic visit), segregated from each other. In another, face-to-face contact was eliminated (e.g., videoconferencing). We also varied clinician-clinician contact; baseline and ongoing "external" infection rates; whether overt symptoms reduced transmission risk behaviourally (e.g., via personal protective equipment, PPE); and household clustering. Results: Service organisation had minimal effects on whole-population infection under our assumptions but materially affected clinician infection. Appointment type and inter-clinician contact had greater effects at low external infection rates and without a behavioural symptom response. Clustering magnified the effect of appointment type. We discuss infection control and other factors affecting appointment choice and team organisation. Conclusions: Distancing between clinicians can have significant effects on team infection. Loss of clinicians to infection likely has an adverse impact on care, not modelled here. Appointments must account for clinical necessity as well as infection control. Interventions to reduce transmission risk can synergize, arguing for maximal distancing and behavioural measures (e.g., PPE) consistent with safe care.