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Register a new userMaximising the Benefits of an Acutely Limited Number of COVID-19 Tests
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We propose a novel testing and containment strategy in order to contain the spread of SARS-CoV2 while permitting large parts of the population to resume social and economic activity. Our approach recognises the fact that testing capacities are severely constrained in many countries. In this setting, we show that finding the best way to utilise this limited number of tests during a pandemic can be formulated concisely as an allocation problem. Our problem formulation takes into account the heterogeneity of the population and uses pooled testing to identify and isolate individuals while prioritising key workers and individuals with a higher risk of spreading the disease. In order to demonstrate the efficacy of our testing and containment mechanism, we perform simulations using a network-based SIR model. Our simulations indicate that applying our mechanism on a population of $100,000$ individuals with only $16$ tests per day reduces the peak number of infected individuals by approximately $20%$, when compared to the scenario where no intervention is implemented.
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Vaccination against COVID-19 with the recently approved mRNA vaccines BNT162b2 (BioNTech/Pfizer) and mRNA-1273 (Moderna) is currently underway in a large number of countries. However, high incidence rates and rapidly spreading SARS-CoV-2 variants are concerning. In combination with acute supply deficits in Europe in early 2021, the question arises of whether stretching the vaccine, for instance by delaying the second dose, can make a significant contribution to preventing deaths, despite associated risks such as lower vaccine efficacy, the potential emergence of escape mutants, enhancement, waning immunity, reduced social acceptance of off-label vaccination, and liability shifts. A quantitative epidemiological assessment of risks and benefits of non-standard vaccination protocols remains elusive. To clarify the situation and to provide a quantitative epidemiological foundation we develop a stochastic epidemiological model that integrates specific vaccine rollout protocols into a risk-group structured infectious disease dynamical model. Using the situation and conditions in Germany as a reference system, we show that delaying the second vaccine dose is expected to prevent deaths in the four to five digit range, should the incidence resurge. We show that this considerable public health benefit relies on the fact that both mRNA vaccines provide substantial protection against severe COVID-19 and death beginning 12 to 14 days after the first dose. The benefits of protocol change are attenuated should vaccine compliance decrease substantially. To quantify the impact of protocol change on vaccination adherence we performed a large-scale online survey. We find that, in Germany, changing vaccination protocols may lead to small reductions in vaccination intention. In sum, we therefore expect the benefits of a strategy change to remain substantial and stable.
The reproductive number R_0 (and its value after initial disease emergence R) has long been used to predict the likelihood of pathogen invasion, to gauge the potential severity of an epidemic, and to set policy around interventions. However, often ignored complexities have generated confusion around use of the metric. This is particularly apparent with the emergent pandemic virus SARS-CoV-2, the causative agent of COVID-19. We address some of these misconceptions, namely, how R changes over time, varies over space, and relates to epidemic size by referencing the mathematical definition of R and examples from the current pandemic. We hope that a better appreciation of the uses, nuances, and limitations of R facilitates a better understanding of epidemic spread, epidemic severity, and the effects of interventions in the context of SARS-CoV-2.
We propose a mathematical model to analyze the time evolution of the total number of infected population with Covid-19 disease at a region in the ongoing pandemic. Using the available data of Covid-19 infected population on various countries we formulate a model which can successfully track the time evolution from early days to the saturation period in a given wave of this infectious disease. It involves a set of effective parameters which can be extracted from the available data. Using those parameters the future trajectories of the disease spread can also be projected. A set of differential equations is also proposed whose solutions are these time evolution trajectories. Using such a formalism we project the future time evolution trajectories of infection spread for a number of countries where the Covid-19 infection is still rapidly rising.
With the unfolding of the COVID-19 pandemic, mathematical modeling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long term predictions were extremely challenging to address. Moreover, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks. Yet a robust modeling of pandemic dynamics and a consistent choice of the transmission metric is crucial for an in-depth understanding of the macroscopic phenomenology and better-informed mitigation strategies. In this study, we propose a Markovian stochastic framework designed to describe the evolution of entropy during the COVID-19 pandemic and the instantaneous reproductive ratio. We then introduce and use entropy-based metrics of global transmission to measure the impact and temporal evolution of a pandemic event. In the formulation of the model, the temporal evolution of the outbreak is modeled by the master equation of a nonlinear Markov process for a statistically averaged individual, leading to a clear physical interpretation. We also provide a full Bayesian inversion scheme for calibration. The time evolution of the entropy rate, the absolute change in the system entropy, and the instantaneous reproductive ratio are natural and transparent outputs of this framework. The framework has the appealing property of being applicable to any compartmental epidemic model. As an illustration, we apply the proposed approach to a simple modification of the Susceptible-Exposed-Infected-Removed (SEIR) model. Applying the model to the Hubei region, South Korean, Italian, Spanish, German, and French COVID-19 data-sets, we discover a significant difference in the absolute change of entropy but highly regular trends for both the entropy evolution and the instantaneous reproductive ratio.
A second wave of SARS-CoV-2 is unfolding in dozens of countries. However, this second wave manifests itself strongly in new reported cases, but less in death counts compared to the first wave. Over the past three months in Germany, the reported cases increased by a factor five or more, whereas the death counts hardly grew. This discrepancy fueled speculations that the rise of reported cases would not reflect a second wave but only wider testing. We find that this apparent discrepancy can be explained to a large extent by the age structure of the infected, and predict a pronounced increase of death counts in the near future, as the spread once again expands into older age groups. To re-establish control, and to avoid the tipping point when TTI capacity is exceeded, case numbers have to be lowered. Otherwise the control of the spread and the protection of vulnerable people will require more restrictive measures latest when the hospital capacity is reached.
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