Quantitative Biology

This paper presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measures used to describe the transmission dynamics of this pandemic. The reproduction number alongside other key parameters of the model can then be estimated by fitting the model to real-world data using numerical optimisation techniques or by inducing ad-hoc control actions as recorded in the news platforms. In this paper, the model is verified using a case study based on the data from the first wave of COVID-19 in the Republic of Kazakhstan. The model is fitted to provide estimates for two settings in simulations; time-invariant and time-varying (with bounded constraints) parameters. Finally, some forecasts are made using four scenarios with time-dependent control measures so as to determine which would reflect on the actual situations better.

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation (ODE) models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased (SEIRD) framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the cancer cells phase into two sub-phases depending on their maturity state. The same approach is also applied for the vasculature phase, which is divided into young sprouts (products of angiogenesis), and fully formed-mature vessels. The remaining two phases correspond to healthy cells and extracellular material (ECM). Furthermore, the model foresees the existence of nutrient chemical species, which are transferred within the tissue through diffusion or supplied by the vasculature (blood vessels). The model is numerically solved with the Finite Elements Method and computations are performed with the commercial software Comsol Multiphysics. The numerical simulations predict that mature cancer cells are well separated from young cancer cells, which form a protective shield for the growing tumor. We study the effect of different mitosis and death rates for mature and young cancer cells on the tumor growth rate, and predict accelerated rates when the mitosis rate of young cancer cells is higher compared to mature cancer cells.

We study the influence of the rate of the attainment of herd immunity (HI), in the absence of an approved vaccine, on the vulnerable population. We essentially ask the question: how hard the evolution towards the desired herd immunity could be on the life of the vulnerables? We employ mathematical modelling (chemical network theory) and cellular automata based computer simulations to study the human cost of an epidemic spread and an effective strategy to introduce HI. Implementation of different strategies to counter the spread of the disease requires a certain degree of quantitative understanding of the time dependence of the outcome. In this paper, our main objective is to gather understanding of the dependence of outcome on the rate of progress of HI. We generalize the celebrated SIR model (Susceptible-Infected-Removed) by compartmentalizing the susceptible population into two categories- (i) vulnerables and (ii) resilients, and study dynamical evolution of the disease progression. We achieve such a classification by employing different rates of recovery of vulnerables vis-a-vis resilients. We obtain the relative fatality of these two sub-categories as a function of the percentages of the vulnerable and resilient population, and the complex dependence on the rate of attainment of herd immunity. Our results quantify the adverse effects on the recovery rates of vulnerables in the course of attaining the herd immunity. We find the important result that a slower attainment of the HI is relatively less fatal. However, a slower progress towards HI could be complicated by many intervening factors.

The Bacille Calmette-Guérin (BCG) tuberculosis vaccine has immunity benefits against respiratory infections. Accordingly, it has been hypothesized that it may have a protective effect against COVID-19. Recent research found that countries with universal Bacillus Calmette-Guérin (BCG) childhood vaccination policies tend to be less affected by the COVID-19 pandemic. However, such ecological studies are biased by numerous confounders. Instead, this paper takes advantage of a rare nationwide natural experiment that took place in Sweden in 1975, where discontinuation of newborns BCG vaccination led to a dramatic fall of the BCG coverage rate from 92% to 2% , thus allowing us to estimate the BCG's effect without all the biases associated with cross-country comparisons. Numbers of COVID-19 cases and hospitalizations were recorded for birth cohorts born just before and just after that change, representing 1,026,304 and 1,018,544 individuals, respectively. We used regression discontinuity to assess the effect of BCG vaccination on Covid-19 related outcomes. This method used on such a large population allows for a high precision that would be hard to achieve using a classical randomized controlled trial. The odds ratio for Covid-19 cases and Covid-19 related hospitalizations were 0.9997 (CI95: [0.8002-1.1992]) and 1.1931 (CI95: [0.7558-1.6304]), respectively. We can thus reject with 95\% confidence that universal BCG vaccination reduces the number of cases by more than 20% and the number of hospitalizations by more than 24%. While the effect of a recent vaccination must be evaluated, we provide strong evidence that receiving the BCG vaccine at birth does not have a protective effect against COVID-19.

We revisit the modeling of the diauxic growth of a pure microorganism on two distinct sugars which was first described by Monod. Most available models are deterministic and make the assumption that all cells of the microbial ecosystem behave homogeneously with respect to both sugars, all consuming the first one and then switching to the second when the first is exhausted. We propose here a stochastic model which describes what is called "metabolic heterogeneity". It allows to consider small populations as in microfluidics as well as large populations where billions of individuals coexist in the medium in a batch or chemostat. We highlight the link between the stochastic model and the deterministic behavior in real large cultures using a large population approximation. Then the influence of model parameter values on model dynamics is studied, notably with respect to the lag-phase observed in real systems depending on the sugars on which the microorganism grows. It is shown that both metabolic parameters as well as initial conditions play a crucial role on system dynamics.

An epidemic carries human and fiscal costs. In the case of imported pandemics, the first-best solution is to restrict national borders to identify and isolate infected individuals. However, when that opportunity is not fully seized and there is no preventative intervention available, second-best options must be chosen. In this article we develop a system of differential equations that simulate both the fiscal and human costs associated to different mitigation measurements. After simulating several scenarios, we conclude that herd immunity (or unleashing the pandemic) is the worst policy in terms of both human and fiscal cost. We found that the second-best policy would be a strict policy (e.g. physical distancing with massive testing) established under the first 20 days after the pandemic, that lowers the probability of infection by 80%. In the case of the US, this strict policy would save more than 239 thousands lives and almost $170.8 billion to taxpayers when compared to the herd immunity case.

In this article, we consider a dynamic epidemiology model for the spread of the COVID-19 infection. Starting from the classical SEIR model, the model is modified so as to better describe characteristic features of the underlying pathogen and its infectious modes. In line with the large number of secondary infections not related to contact with documented infectious individuals, the model includes a cohort of asymptomatic or oligosymptomatic infectious individuals, not accounted for in the data of new daily counts of infections. A Bayesian particle filtering algorithm is used to update dynamically the relevant cohort and simultaneously estimate the transmission rate as the new data on the number of new infections and disease related death become available. The underlying assumption of the model is that the infectivity rate is dynamically changing during the epidemics, either because of a mutation of the pathogen or in response to mitigation and containment measures. The sequential Bayesian framework naturally provides a quantification of the uncertainty in the estimate of the model parameters, including the reproduction number, and of the size of the different cohorts. Moreover, we introduce a dimensionless quantity, which is the equilibrium ratio between asymptomatic and symptomatic cohort sizes, and propose a simple formula to estimate the quantity. This ratio leads naturally to another dimensionless quantity that plays the role of the basic reproduction number R 0 of the model. When we apply the model and particle filter algorithm to COVID-19 infection data from several counties in Northeastern Ohio and Southeastern Michigan we found the proposed reproduction number R 0 to have a consistent dynamic behavior within both states, thus proving to be a reliable summary of the success of the mitigation measures.

Understanding the consequences of the combined effects of multiple stressors-including stress from man-made chemicals is important for conservation management, the ecological risk assessment of chemicals, and many other ecological applications. Our current ability to predict and analyse the joint effects of multiple stressors is insufficient to make the prospective risk assessment of chemicals more ecologically relevant because we lack a full understanding of how organisms respond to stress factors alone and in combination. Here, we describe a Dynamic Energy Budget (DEB) based bioenergetics model that predicts the potential effects of single or multiple natural and chemical stressors on life history traits. We demonstrate the plausibility of the model using a meta-analysis of 128 existing studies on freshwater invertebrates. We then validate our model by comparing its predictions for a combination of three stressors (i.e. chemical, temperature, and food availability) with new, independent experimental data on life history traits in the daphnid Ceriodaphnia dubia. We found that the model predictions are in agreement with observed growth curves and reproductive traits. To the best of our knowledge, this is the first time that the combined effects of three stress factors on life history traits observed in laboratory studies have been predicted successfully in invertebrates. We suggest that a re-analysis of existing studies on multiple stressors within the modelling framework outlined here will provide a robust null model for identifying stressor interactions, and expect that a better understanding of the underlying mechanisms will arise from these new analyses. Bioenergetics modelling could be applied more broadly to support environmental management decision making.

This paper extends the canonical model of epidemiology, SIRD model, to allow for time varying parameters for real-time measurement of the stance of the COVID-19 pandemic. Time variation in model parameters is captured using the generalized autoregressive score modelling structure designed for the typically daily count data related to pandemic. The resulting specification permits a flexible yet parsimonious model structure with a very low computational cost. This is especially crucial at the onset of the pandemic when the data is scarce and the uncertainty is abundant. Full sample results show that countries including US, Brazil and Russia are still not able to contain the pandemic with the US having the worst performance. Furthermore, Iran and South Korea are likely to experience the second wave of the pandemic. A real-time exercise show that the proposed structure delivers timely and precise information on the current stance of the pandemic ahead of the competitors that use rolling window. This, in turn, transforms into accurate short-term predictions of the active cases. We further modify the model to allow for unreported cases. Results suggest that the effects of the presence of these cases on the estimation results diminish towards the end of sample with the increasing number of testing.