A Hybridized Stochastic SIR-Vasicek Model in Evaluating a Pandemic Emergency Financing Facility

In the context of the present global health crisis, we examine the design and valuation of a pandemic emergency financing facility (PEFF) akin to a catastrophe (CAT) bond. While a CAT bond typically enables fund generation to the insurers and re-insurers after a disaster happens, a PEFF or pandemic bond's payout is linked to random thresholds that keep evolving as the pandemic continues to unfold. The subtle difference in the timing and structure of the funding payout between the usual CAT bond and PEFF complicates the valuation of the latter. We address this complication, and our analysis identifies certain aspects in the PEFF's design that must be simplified and strengthened so that this financial instrument is able to serve the intent of its original creation. An extension of the compartmentalized deterministic epidemic model-which describes the random number of people in three classes: susceptible (S), infected (I), and removed (R) or SIR for short-to its stochastic analog is put forward. At time t, S(t), I(t), and R (t) satisfy a system of interacting stochastic differential equations in our extended framework. The payout is triggered when the number of infected people exceeds a predetermined threshold. A CAT-bond pricing setup is developed with the Vasicek-based financial risk factor correlated with the SIR dynamics for the PEFF valuation. The probability of a pandemic occurrence during the bond's term to maturity is calculated via a Poisson process. Our sensitivity analyses reveal that the SIR's disease transmission and recovery rates, as well as the interest rate's mean-reverting level, have a substantial effect on the bond price. Our proposed synthesized model was tested and validated using a Canadian COVID-19 dataset during the early development of the pandemic. We illustrate that the PEFF's payout could occur as early as seven weeks after the official declaration of the pandemic, and the deficiencies of the most recent PEFF sold by an international financial institution could be readily rectified.

Flattening the curve

We quantify attening the curve under the assumption of a soft quarantine in the spread of a contagious viral disease in a society. In particular, the maximum daily infection rate is expected to drop by twice the percentage drop in the virus reproduction number. The same percentage drop is expected for the maximum daily hospitalization or fatality rate. A formula for the expected maximum daily fatality rate is given. (PsycInfo Database Record (c) 2023 APA, all rights reserved)

Modeling the impact of the Omicron infection wave in Germany.

In November 2021, the first infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant of concern (VOC) B.1.1.529 ('Omicron') was reported in Germany, alongside global reports of reduced vaccine efficacy (VE) against infections with this variant. The potential threat posed by its rapid spread in Germany was, at the time, difficult to predict. We developed a variant-dependent population-averaged susceptible-exposed-infected-recovered infectious-disease model that included information about variant-specific and waning VEs based on empirical data available at the time. Compared to other approaches, our method aimed for minimal structural and computational complexity and therefore enabled us to respond to changes in the situation in a more agile manner while still being able to analyze the potential influence of (non-)pharmaceutical interventions (NPIs) on the emerging crisis. Thus, the model allowed us to estimate potential courses of upcoming infection waves in Germany, focusing on the corresponding burden on intensive care units (ICUs), the efficacy of contact reduction strategies, and the success of the booster vaccine rollout campaign. We expected a large cumulative number of infections with the VOC Omicron in Germany with ICU occupancy likely remaining below capacity, nevertheless, even without additional NPIs. The projected figures were in line with the actual Omicron waves that were subsequently observed in Germany with respective peaks occurring in mid-February and mid-March. Most surprisingly, our model showed that early, strict, and short contact reductions could have led to a strong 'rebound' effect with high incidences after the end of the respective NPIs, despite a potentially successful booster campaign. The results presented here informed legislation in Germany. The methodology developed in this study might be used to estimate the impact of future waves of COVID-19 or other infectious diseases.

Assessing the accuracy of California county level COVID-19 hospitalization forecasts to inform public policy decision making.

BACKGROUND: The COVID-19 pandemic has highlighted the role of infectious disease forecasting in informing public policy. However, significant barriers remain for effectively linking infectious disease forecasts to public health decision making, including a lack of model validation. Forecasting model performance and accuracy should be evaluated retrospectively to understand under which conditions models were reliable and could be improved in the future. METHODS: Using archived forecasts from the California Department of Public Health's California COVID Assessment Tool ( https://calcat.covid19.ca.gov/cacovidmodels/ ), we compared how well different forecasting models predicted COVID-19 hospitalization census across California counties and regions during periods of Alpha, Delta, and Omicron variant predominance. RESULTS: Based on mean absolute error estimates, forecasting models had variable performance across counties and through time. When accounting for model availability across counties and dates, some individual models performed consistently better than the ensemble model, but model rankings still differed across counties. Local transmission trends, variant prevalence, and county population size were informative predictors for determining which model performed best for a given county based on a random forest classification analysis. Overall, the ensemble model performed worse in less populous counties, in part because of fewer model contributors in these locations. CONCLUSIONS: Ensemble model predictions could be improved by incorporating geographic heterogeneity in model coverage and performance. Consistency in model reporting and improved model validation can strengthen the role of infectious disease forecasting in real-time public health decision making.

Effect of Transmission and Vaccination on Time to Dominance of Emerging Viral Strains: A Simulation-Based Study.

We studied the effect of transmissibility and vaccination on the time required for an emerging strain of an existing virus to dominate in the infected population using a simulation-based experiment. The emergent strain is assumed to be completely resistant to the available vaccine. A stochastic version of a modified SIR model for emerging viral strains was developed to simulate surveillance data for infections. The proportion of emergent viral strain infections among the infected was modeled using a logistic curve and the time to dominance (TTD) was recorded for each simulation. A factorial experiment was implemented to compare the TTD values for different transmissibility coefficients, vaccination rates, and initial vaccination coverage. We discovered a non-linear relationship between TTD and the relative transmissibility of the emergent strain for populations with low vaccination coverage. Furthermore, higher vaccination coverage and high vaccination rates in the population yielded significantly lower TTD values. Vaccinating susceptible individuals against the current strain increases the susceptible pool of the emergent virus, which leads to the emergent strain spreading faster and requiring less time to dominate the infected population.

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.

The changing health impact of vaccines in the COVID-19 pandemic: A modeling study.

Much of the world's population had already been infected with COVID-19 by the time the Omicron variant emerged at the end of 2021, but the scale of the Omicron wave was larger than any that had come before or has happened since, and it left a global imprinting of immunity that changed the COVID-19 landscape. In this study, we simulate a South African population and demonstrate how population-level vaccine effectiveness and efficiency changed over the course of the first 2 years of the pandemic. We then introduce three hypothetical variants and evaluate the impact of vaccines with different properties. We find that variant-chasing vaccines have a narrow window of dominating pre-existing vaccines but that a variant-chasing vaccine strategy may have global utility, depending on the rate of spread from setting to setting. Next-generation vaccines might be able to overcome uncertainty in pace and degree of viral evolution.

Impact of early phase COVID-19 precautionary behaviors on seasonal influenza in Hong Kong: A time-series modeling approach.

Background: Before major non-pharmaceutical interventions were implemented, seasonal incidence of influenza in Hong Kong showed a rapid and unexpected reduction immediately following the early spread of COVID-19 in mainland China in January 2020. This decline was presumably associated with precautionary behavioral changes (e.g., wearing face masks and avoiding crowded places). Knowing their effectiveness on the transmissibility of seasonal influenza can inform future influenza prevention strategies. Methods: We estimated the effective reproduction number (R t ) of seasonal influenza in 2019/20 winter using a time-series susceptible-infectious-recovered (TS-SIR) model with a Bayesian inference by integrated nested Laplace approximation (INLA). After taking account of changes in underreporting and herd immunity, the individual effects of the behavioral changes were quantified. Findings: The model-estimated mean R t reduced from 1.29 (95%CI, 1.27-1.32) to 0.73 (95%CI, 0.73-0.74) after the COVID-19 community spread began. Wearing face masks protected 17.4% of people (95%CI, 16.3-18.3%) from infections, having about half of the effect as avoiding crowded places (44.1%, 95%CI, 43.5-44.7%). Within the current model, if more than 85% of people had adopted both behaviors, the initial R t could have been less than 1. Conclusion: Our model results indicate that wearing face masks and avoiding crowded places could have potentially significant suppressive impacts on influenza.

Modeling the impact of child vaccination (5-11 y) on overall COVID-19 related hospitalizations and mortality in a context of omicron variant predominance and different vaccination coverage paces in Brazil.

Background: Developing countries have experienced significant COVID-19 disease burden. With the emergence of new variants, particularly omicron, the disease burden in children has increased. When the first COVID-19 vaccine was approved for use in children aged 5-11 years of age, very few countries recommended vaccination due to limited risk-benefit evidence for vaccination of this population. In Brazil, ranking second in the global COVID-19 death toll, the childhood COVID-19 disease burden increased significantly in early 2022. This prompted a risk-benefit assessment of the introduction and scaling-up of COVID-19 vaccination of children. Methods: To estimate the potential impact of vaccinating children aged 5-11 years with mRNA-based COVID-19 vaccine in the context of omicron dominance, we developed a discrete-time SEIR-like model stratified in age groups, considering a three-month time horizon. We considered three scenarios: No vaccination, slow, and maximum vaccination paces. In each scenario, we estimated the potential reduction in total COVID-19 cases, hospitalizations, deaths, hospitalization costs, and potential years of life lost, considering the absence of vaccination as the base-case scenario. Findings: We estimated that vaccinating at a maximum pace could prevent, between mid-January and April 2022, about 26,000 COVID-19 hospitalizations, and 4200 deaths in all age groups; of which 5400 hospitalizations and 410 deaths in children aged 5-11 years. Continuing vaccination at a slow/current pace would prevent 1450 deaths and 9700 COVID-19 hospitalizations in all age groups in this same time period; of which 180 deaths and 2390 hospitalizations in children only. Interpretation: Maximum vaccination of children results in a significant reduction of COVID-19 hospitalizations and deaths and should be enforced in developing countries with significant disease incidence in children. Funding: This manuscript was funded by the Brazilian Council for Scientific and Technology Development (CNPq - Process # 402834/2020-8).

Modeling COVID-19 incidence with Google Trends.

Infodemiologic methods could be used to enhance modeling infectious diseases. It is of interest to verify the utility of these methods using a Nigerian case study. We used Google Trends data to track COVID-19 incidences and assessed whether they could complement traditional data based solely on reported case numbers. Data on the Nigerian weekly COVID-19 cases spanning through March 1, 2020, to May 31, 2021, were matched with internet search data from Google Trends. The reported weekly incidence numbers and the GT data were split into training and testing sets. ARIMA models were fitted to describe reported weekly COVID cases using the training set. Several COVID-related search terms were theoretically and empirically assessed for initial screening. The utilized Google Trends (GT) variable was added to the ARIMA model as a regressor. Model forecasts, both with and without GTD, were compared with weekly cases in the test set over 13 weeks. Forecast accuracies were compared visually and using RMSE (root mean square error) and MAE (mean average error). Statistical significance of the difference in predictions was determined with the two-sided Diebold-Mariano test. Preliminary results of contemporaneous correlations between COVID-related search terms and weekly COVID cases reveal "loss of smell," "loss of taste," "fever" (in order of magnitude) as significantly associated with the official cases. Predictions of the ARIMA model using solely reported case numbers resulted in an RMSE (root mean squared error) of 411.4 and mean absolute error (MAE) of 354.9. The GT expanded model achieved better forecasting accuracy (RMSE: 388.7 and MAE = 340.1). Corrected Akaike Information Criteria also favored the GT expanded model (869.4 vs. 872.2). The difference in predictive performances was significant when using a two-sided Diebold-Mariano test (DM = 6.75, p < 0.001) for the 13 weeks. Google trends data enhanced the predictive ability of a traditionally based model and should be considered a suitable method to enhance infectious disease modeling.

Flattening the curve

We quantify attening the curve under the assumption of a soft quarantine in the spread of a contagious viral disease in a society. In particular, the maximum daily infection rate is expected to drop by twice the percentage drop in the virus reproduction number. The same percentage drop is expected for the maximum daily hospitalization or fatality rate. A formula for the expected maximum daily fatality rate is given. (PsycInfo Database Record (c) 2022 APA, all rights reserved)

Predicting Future, Past, and Misinterpreted COVID-19 Cases Using Bidirectional LSTM Model for Proper Health Monitoring: Advances in Data Analytics

The first coronavirus case was reported in Hubei province of China, and within three months, it affected almost all the countries in the world. under such circumstances, World Health Organization (WHO) declared 2019 novel coronavirus as a global pandemic. Even though its fatality is low, the transmission rate makes it more dangerous. Similar to previous disease outbreaks in the human history, COVID-19 also exhibits certain transmission patterns. Mathematical models can be used to analyze these patterns and forecast the upcoming COVID-19 cases. Such forecasting methods could help governments to take further actions to stop those cases from occurring. Most of the previous studies used past infections to forecast future infections. However, they completely neglected the unreported cases while making predictions. By knowing the initially reported cases, we can understand the dynamics of the epidemic more precisely. In order to capture the transmission dynamics, we proposed a novel deep learning model called a B-LSTM (Bidirectional Long Short-Term Memory) model. In order to recalculate the past or missing infections, we applied a masking technique to our B-LSTM model. Results obtained from our model shows that end point of this pandemic in India will be around next year. However, by November the rate of infections will decrease linearly. In addition to that, we compared the forecasting accuracies of B-LSTM with statistical-based ARIMA and LSTM models. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Effect of COVID-19 driven lockdown on social contact pattern in Puducherry, India: A longitudinal study.

Objective: This study was undertaken to assess the change in social contact and transmission dynamics among adults in the Puducherry district during the different phases of country-wide lockdown. Methods: Adults aged 18-69 years in Puducherry were assessed for frequency and duration of contacts in the following time points: prior to lockdown (March 2020), during lockdown, immediate post-lockdown (April, June 2020), and seven months post-lockdown (February 2021). Adjusted incidence rate ratios (aIRR) were obtained using a generalized estimating equation. We also assessed the exponential trajectory of the time-varying reproduction number (Rt) during and after lockdown. Results: Compared to pre-lockdown phase, frequency of social contacts during 1st week, 4th week of lockdown, and immediate post-lockdown were reduced by 89% (aIRR = 0.11; 95% CI: 0.09-0.13), 40% (aIRR = 0.60; 95% CI: 0.52-0.69) and 91% (aIRR = 0.09; 95% CI: 0.07-0.10) respectively. However, the decline was not statistically significant at seven months post-lockdown. Correspondingly, we observed an initial spike in Rt during the lockdown phase followed by a gradual decline during the immediate post-lockdown phase. However, seven months post-lockdown, Rt has increased again. Conclusion: The study showed high compliance to the lockdown measures in Puducherry during the lockdown and immediate post-lockdown periods. However, as the lockdown measures were relaxed, the contact rate returned to the pre-lockdown state.

Evaluating effectiveness of public health intervention strategies for mitigating COVID-19 pandemic.

Coronavirus disease 2019 (COVID-19) pandemic is an unprecedented global public health challenge. In the United States (US), state governments have implemented various non-pharmaceutical interventions (NPIs), such as physical distance closure (lockdown), stay-at-home order, mandatory facial mask in public in response to the rapid spread of COVID-19. To evaluate the effectiveness of these NPIs, we propose a nested case-control design with propensity score weighting under the quasi-experiment framework to estimate the average intervention effect on disease transmission across states. We further develop a method to test for factors that moderate intervention effect to assist precision public health intervention. Our method takes account of the underlying dynamics of disease transmission and balance state-level pre-intervention characteristics. We prove that our estimator provides causal intervention effect under assumptions. We apply this method to analyze US COVID-19 incidence cases to estimate the effects of six interventions. We show that lockdown has the largest effect on reducing transmission and reopening bars significantly increase transmission. States with a higher percentage of non-White population are at greater risk of increased R t $$ {R}_t $$ associated with reopening bars.

Impact of implementation timing on the effectiveness of stay-at-home requirement under the COVID-19 pandemic: Lessons from the Italian Case.

When a new infectious outbreak emerges, governments must initially rely on non-pharmaceutical interventions (NPIs) to mitigate the impact of the pathogen. Although a strict stay-at-home requirement (i.e., lockdown) presents high effectiveness in reducing patients hospitalized in intensive care units (ICUs), it comes with unintended physical, psychological, and economic damages for the citizens. Using how Italy managed the COVID-19 outbreak from February to September 2020 on a national basis, this study aims at understanding the impact of implementation timing on the effectiveness of NPIs. Our findings may be helpful to avoid the implementation of stay-at-home requirements when it is not strictly necessary. A compartmental SEICRD model was developed to create the baseline scenario without NPIs. Generalized Poisson regressions were applied to study the change in effectiveness over-time of NPIs on Avoided ICUs for each one of the Italian regions. Our study suggests that although the stay-at-home requirement is the most effective measure in reducing ICU hospitalizations in regions encountering the outbreak early, its effectiveness decreases in regions encountering the outbreak later, where a set of other NPIs are more effective. We developed a reference of daily new cases when lockdown should be implemented or avoided, accordingly. Our findings could be useful to support policymakers in contrasting the pandemic and in limiting the societal and economic impact of stringent NPIs.

Heterologous vaccination interventions to reduce pandemic morbidity and mortality: Modeling the US winter 2020 COVID-19 wave.

COVID-19 remains a stark health threat worldwide, in part because of minimal levels of targeted vaccination outside high-income countries and highly transmissible variants causing infection in vaccinated individuals. Decades of theoretical and experimental data suggest that nonspecific effects of non-COVID-19 vaccines may help bolster population immunological resilience to new pathogens. These routine vaccinations can stimulate heterologous cross-protective effects, which modulate nontargeted infections. For example, immunization with Bacillus Calmette-Guérin, inactivated influenza vaccine, oral polio vaccine, and other vaccines have been associated with some protection from SARS-CoV-2 infection and amelioration of COVID-19 disease. If heterologous vaccine interventions (HVIs) are to be seriously considered by policy makers as bridging or boosting interventions in pandemic settings to augment nonpharmaceutical interventions and specific vaccination efforts, evidence is needed to determine their optimal implementation. Using the COVID-19 International Modeling Consortium mathematical model, we show that logistically realistic HVIs with low (5 to 15%) effectiveness could have reduced COVID-19 cases, hospitalization, and mortality in the United States fall/winter 2020 wave. Similar to other mass drug administration campaigns (e.g., for malaria), HVI impact is highly dependent on both age targeting and intervention timing in relation to incidence, with maximal benefit accruing from implementation across the widest age cohort when the pandemic reproduction number is >1.0. Optimal HVI logistics therefore differ from optimal rollout parameters for specific COVID-19 immunizations. These results may be generalizable beyond COVID-19 and the US to indicate how even minimally effective heterologous immunization campaigns could reduce the burden of future viral pandemics.

A Hybridized Stochastic SIR-Vasiček Model in Evaluating a Pandemic Emergency Financing Facility

In the context of the present global health crisis, we examine the design and valuation of a pandemic emergency financing facility (PEFF) akin to a catastrophe (CAT) bond. While a CAT bond typically enables fund generation to the insurers and re-insurers after a disaster happens, a PEFF or pandemic bond's payout is linked to random thresholds that keep evolving as the pandemic continues to unfold. The subtle difference in the timing and structure of the funding payout between the usual CAT bond and PEFF complicates the valuation of the latter. We address this complication, and our analysis identifies certain aspects in the PEFF's design that must be simplified and strengthened so that this financial instrument is able to serve the intent of its original creation. An extension of the compartmentalized deterministic epidemic model--which describes the random number of people in three classes: susceptible (S), infected (I), and removed (R) or SIR for short--to its stochastic analog is put forward. At time t, S(t), I(t), and R(t) satisfy a system of interacting stochastic differential equations in our extended framework. The payout is triggered when the number of infected people exceeds a predetermined threshold. A CAT-bond pricing setup is developed with the Vasiček-based financial risk factor correlated with the SIR dynamics for the PEFF valuation. The probability of a pandemic occurrence during the bond's term to maturity is calculated via a Poisson process. Our sensitivity analyses reveal that the SIR's disease transmission and recovery rates, as well as the interest rate's mean-reverting level, have a substantial effect on the bond price. Our proposed synthesized model was tested and validated using a Canadian COVID-19 dataset during the early development of the pandemic. We illustrate that the PEFF's payout could occur as early as seven weeks after the official declaration of the pandemic, and the deficiencies of the most recent PEFF sold by an international financial institution could be readily rectified. IEEE

Age-stratified transmission model of COVID-19 in Ontario with human mobility during pandemic's first wave.

In this work, we employ a data-fitted compartmental model to visualize the progression and behavioral response to COVID-19 that match provincial case data in Ontario, Canada from February to June of 2020. This is a "rear-view mirror" glance at how this region has responded to the 1st wave of the pandemic, when testing was sparse and NPI measures were the only remedy to stave off the pandemic. We use an SEIR-type model with age-stratified subpopulations and their corresponding contact rates and asymptomatic rates in order to incorporate heterogeneity in our population and to calibrate the time-dependent reduction of Ontario-specific contact rates to reflect intervention measures in the province throughout lockdown and various stages of social-distancing measures. Cellphone mobility data taken from Google, combining several mobility categories, allows us to investigate the effects of mobility reduction and other NPI measures on the evolution of the pandemic. Of interest here is our quantification of the effectiveness of Ontario's response to COVID-19 before and after provincial measures and our conclusion that the sharp decrease in mobility has had a pronounced effect in the first few weeks of the lockdown, while its effect is harder to infer once other NPI measures took hold.

A simple model for how the risk of pandemics from different virus families depends on viral and human traits.

Different virus families, like influenza or corona viruses, exhibit characteristic traits such as typical modes of transmission and replication as well as specific animal reservoirs in which each family of viruses circulate. These traits of genetically related groups of viruses influence how easily an animal virus can adapt to infect humans, how well novel human variants can spread in the population, and the risk of causing a global pandemic. Relating the traits of virus families to their risk of causing future pandemics, and identification of the key time scales within which public health interventions can control the spread of a new virus that could cause a pandemic, are obviously significant. We address these issues using a minimal model whose parameters are related to characteristic traits of different virus families. A key trait of viruses that "spillover" from animal reservoirs to infect humans is their ability to propagate infection through the human population (fitness). We find that the risk of pandemics emerging from virus families characterized by a wide distribution of the fitness of spillover strains is much higher than if such strains were characterized by narrow fitness distributions around the same mean. The dependences of the risk of a pandemic on various model parameters exhibit inflection points. We find that these inflection points define informative thresholds. For example, the inflection point in variation of pandemic risk with time after the spillover represents a threshold time beyond which global interventions would likely be too late to prevent a pandemic.