The Signature Features of COVID-19 Pandemic in a Hybrid Mathematical Model-Implications for Optimal Work-School Lockdown Policy

Cost-optimal seeding strategy during a botanical pandemic in domesticated fields

Botanical pandemics cause enormous economic damage and food shortages around the globe. However, since botanical pandemics are here to stay in the short-medium term, domesticated field owners can strategically seed their fields to optimize each session's economic profit. In this work, we propose a novel epidemiological-economic mathematical model that describes the economic profit from a field of plants during a botanical pandemic. We describe the epidemiological dynamics using a spatiotemporal extended susceptible-infected-recovered epidemiological model with a non-linear output economic model. We provide an algorithm to obtain an optimal grid-formed seeding strategy to maximize economic profit, given field and pathogen properties. We show that the recovery and basic infection rates have a similar economic influence. Unintuitively, we show that a larger farm does not promise higher economic profit. Our results demonstrate a significant benefit of using the proposed seeding strategy and shed more light on the dynamics of the botanical pandemic.

Bounding pandemic spread by heat spread

The beginning of a pandemic is a crucial stage for policymakers. Proper management at this stage can reduce overall health and economical damage. However, knowledge about the pandemic is insufficient. Thus, the use of complex and sophisticated models is challenging. In this study, we propose analytical and stochastic heat spread-based boundaries for the pandemic spread as indicated by the Susceptible-Infected-Recovered (SIR) model. We study the spread of a pandemic on an interaction (social) graph as a diffusion and compared it with the stochastic SIR model. The proposed boundaries are not requiring accurate biological knowledge such as the SIR model does.

Modeling a decision support system for Covid-19 using systems dynamics and fuzzy inference

Covid-19 has impacted the lives of people across the world with deaths and unprecedented economic damage. Countries have employed various restrictions and lockdowns to slow down the rate of its spread with varying degrees of success. This research aims to propose an optimal strategy for dealing with a pandemic taking the deaths and economy into account. A complete lockdown until vaccination is not suitable as it can destroy the economy, whereas having no restrictions would result in more Covid-19 cases. Therefore, there is a need for a dynamic model which can propose a suitable strategy depending on the economic and health situation. This paper discusses an approach involving a systems dynamics model for evaluating deaths and hospitals and a fuzzy inference system for deciding the strategy for the next time period based on pre-defined rules. We estimated Gross Domestic Product (GDP) as a sum of government spending, investment, consumption, and spending. The resulting hybrid framework aims to attain a balance between health and economy during a pandemic. The results from a 30-week simulation indicate that the model has 2.9 million $ in GDP higher than complete lockdown and 21 fewer deaths compared to a scenario with no restrictions. The model can be used for the decision-making of restriction policies by configuring the fuzzy rules and membership functions. The paper also discusses the possibility of introducing virus variants in the model.

Optimizing Spatio-Temporal Allocation of the COVID-19 Vaccine Under Different Epidemiological Landscapes

An efficient and safe vaccine is expected to allow people to return to normal life as soon as possible. However, vaccines for new diseases are likely to be in short supply during the initial deployment due to narrow production capacity and logistics. There is an urgent need to optimize the allocation of limited vaccines to improve the population effectiveness of vaccination. Existing studies mostly address a single epidemiological landscape. The robustness of the effectiveness of other proposed strategies is difficult to guarantee under other landscapes. In this study, a novel vaccination allocation model based on spatio-temporal heterogeneity of epidemiological landscapes is proposed. This model was combined with optimization algorithms to determine the near-optimal spatio-temporal allocation for vaccines with different effectiveness and coverage. We fully simulated the epidemiological landscapes during vaccination, and then minimized objective functions independently under various epidemiological landscapes and degrees of viral transmission. We find that if all subregions are in the middle or late stages of the pandemic, the difference between the effectiveness of the near-optimal and pro-rata strategies is very small in most cases. In contrast, under other epidemiological landscapes, when minimizing deaths, the optimizer tends to allocate the remaining doses to sub-regions with relatively higher risk and expected coverage after covering the elderly. While to minimize symptomatic infections, allocating vaccines first to the higher-risk sub-regions is near-optimal. This means that the pro-rata allocation is a good option when the subregions are all in the middle to late stages of the pandemic. Moreover, we suggest that if all subregions are in the period of rapid virus transmission, vaccines should be administered to older adults in all subregions simultaneously, while when the epidemiological dynamics of the subregions are significantly different, priority can be given to older adults in subregions that are still in the early stages of the pandemic. After covering the elderly in the region, high-risk sub-regions can be prioritized.

Generic approach for mathematical model of multi-strain pandemics

Multi-strain pandemics have emerged as a major concern. We introduce a new model for assessing the connection between multi-strain pandemics and mortality rate, basic reproduction number, and maximum infected individuals. The proposed model provides a general mathematical approach for representing multi-strain pandemics, generalizing for an arbitrary number of strains. We show that the proposed model fits well with epidemiological historical world health data over a long time period. From a theoretical point of view, we show that the increasing number of strains increases logarithmically the maximum number of infected individuals and the mean mortality rate. Moreover, the mean basic reproduction number is statistically identical to the single, most aggressive pandemic strain for multi-strain pandemics.

Measures implemented in the school setting to contain the COVID-19 pandemic

BACKGROUND

In response to the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the impact of coronavirus disease 2019 (COVID-19), governments have implemented a variety of measures to control the spread of the virus and the associated disease. Among these, have been measures to control the pandemic in primary and secondary school settings.

OBJECTIVES

To assess the effectiveness of measures implemented in the school setting to safely reopen schools, or keep schools open, or both, during the COVID-19 pandemic, with particular focus on the different types of measures implemented in school settings and the outcomes used to measure their impacts on transmission-related outcomes, healthcare utilisation outcomes, other health outcomes as well as societal, economic, and ecological outcomes.  SEARCH METHODS: We searched the Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE, Embase, and the Educational Resources Information Center, as well as COVID-19-specific databases, including the Cochrane COVID-19 Study Register and the WHO COVID-19 Global literature on coronavirus disease (indexing preprints) on 9 December 2020. We conducted backward-citation searches with existing reviews.

SELECTION CRITERIA

We considered experimental (i.e. randomised controlled trials; RCTs), quasi-experimental, observational and modelling studies assessing the effects of measures implemented in the school setting to safely reopen schools, or keep schools open, or both, during the COVID-19 pandemic. Outcome categories were (i) transmission-related outcomes (e.g. number or proportion of cases); (ii) healthcare utilisation outcomes (e.g. number or proportion of hospitalisations); (iii) other health outcomes (e.g. physical, social and mental health); and (iv) societal, economic and ecological outcomes (e.g. costs, human resources and education). We considered studies that included any population at risk of becoming infected with SARS-CoV-2 and/or developing COVID-19 disease including students, teachers, other school staff, or members of the wider community.  DATA COLLECTION AND ANALYSIS: Two review authors independently screened titles, abstracts and full texts. One review author extracted data and critically appraised each study. One additional review author validated the extracted data. To critically appraise included studies, we used the ROBINS-I tool for quasi-experimental and observational studies, the QUADAS-2 tool for observational screening studies, and a bespoke tool for modelling studies. We synthesised findings narratively. Three review authors made an initial assessment of the certainty of evidence with GRADE, and several review authors discussed and agreed on the ratings.

MAIN RESULTS

We included 38 unique studies in the analysis, comprising 33 modelling studies, three observational studies, one quasi-experimental and one experimental study with modelling components. Measures fell into four broad categories: (i) measures reducing the opportunity for contacts; (ii) measures making contacts safer; (iii) surveillance and response measures; and (iv) multicomponent measures. As comparators, we encountered the operation of schools with no measures in place, less intense measures in place, single versus multicomponent measures in place, or closure of schools. Across all intervention categories and all study designs, very low- to low-certainty evidence ratings limit our confidence in the findings. Concerns with the quality of modelling studies related to potentially inappropriate assumptions about the model structure and input parameters, and an inadequate assessment of model uncertainty. Concerns with risk of bias in observational studies related to deviations from intended interventions or missing data. Across all categories, few studies reported on implementation or described how measures were implemented. Where we describe effects as 'positive', the direction of the point estimate of the effect favours the intervention(s); 'negative' effects do not favour the intervention.  We found 23 modelling studies assessing measures reducing the opportunity for contacts (i.e. alternating attendance, reduced class size). Most of these studies assessed transmission and healthcare utilisation outcomes, and all of these studies showed a reduction in transmission (e.g. a reduction in the number or proportion of cases, reproduction number) and healthcare utilisation (i.e. fewer hospitalisations) and mixed or negative effects on societal, economic and ecological outcomes (i.e. fewer number of days spent in school). We identified 11 modelling studies and two observational studies assessing measures making contacts safer (i.e. mask wearing, cleaning, handwashing, ventilation). Five studies assessed the impact of combined measures to make contacts safer. They assessed transmission-related, healthcare utilisation, other health, and societal, economic and ecological outcomes. Most of these studies showed a reduction in transmission, and a reduction in hospitalisations; however, studies showed mixed or negative effects on societal, economic and ecological outcomes (i.e. fewer number of days spent in school). We identified 13 modelling studies and one observational study assessing surveillance and response measures, including testing and isolation, and symptomatic screening and isolation. Twelve studies focused on mass testing and isolation measures, while two looked specifically at symptom-based screening and isolation. Outcomes included transmission, healthcare utilisation, other health, and societal, economic and ecological outcomes. Most of these studies showed effects in favour of the intervention in terms of reductions in transmission and hospitalisations, however some showed mixed or negative effects on societal, economic and ecological outcomes (e.g. fewer number of days spent in school). We found three studies that reported outcomes relating to multicomponent measures, where it was not possible to disaggregate the effects of each individual intervention, including one modelling, one observational and one quasi-experimental study. These studies employed interventions, such as physical distancing, modification of school activities, testing, and exemption of high-risk students, using measures such as hand hygiene and mask wearing. Most of these studies showed a reduction in transmission, however some showed mixed or no effects.   As the majority of studies included in the review were modelling studies, there was a lack of empirical, real-world data, which meant that there were very little data on the actual implementation of interventions.

AUTHORS' CONCLUSIONS

Our review suggests that a broad range of measures implemented in the school setting can have positive impacts on the transmission of SARS-CoV-2, and on healthcare utilisation outcomes related to COVID-19. The certainty of the evidence for most intervention-outcome combinations is very low, and the true effects of these measures are likely to be substantially different from those reported here. Measures implemented in the school setting may limit the number or proportion of cases and deaths, and may delay the progression of the pandemic. However, they may also lead to negative unintended consequences, such as fewer days spent in school (beyond those intended by the intervention). Further, most studies assessed the effects of a combination of interventions, which could not be disentangled to estimate their specific effects. Studies assessing measures to reduce contacts and to make contacts safer consistently predicted positive effects on transmission and healthcare utilisation, but may reduce the number of days students spent at school. Studies assessing surveillance and response measures predicted reductions in hospitalisations and school days missed due to infection or quarantine, however, there was mixed evidence on resources needed for surveillance. Evidence on multicomponent measures was mixed, mostly due to comparators. The magnitude of effects depends on multiple factors. New studies published since the original search date might heavily influence the overall conclusions and interpretation of findings for this review.

Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models

We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the Susceptible-Infectious-Recovered (SIR)-type epidemiological model that we developed for viral diseases with long-term immunity memory. This is a large-scale model containing 15 nonlinear ordinary differential equations (ODEs), and classical methods have failed to analytically obtain its equilibria. The proposed method is used to conduct a comprehensive analysis by a stochastic representation of the dynamics of the model, followed by finding all asymptotic stable equilibrium states of the model for any values of parameters and initial conditions thanks to the symmetry of the population size over time.