pwc-archive/papers-with-abstracts huggingface dataset:
SIS Epidemic Model: Birth-and-Death Markov Chain Approach
Authors: A. H. Nzokem
Date: 2021-02-17 00:00:00

We are interested in describing the infected size of the SIS Epidemic model using Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) model is defined within a population of constant size $M$; the size is kept constant by replacing each death with a newborn healthy individual. The life span of each individual in the population is modelled by an exponential distribution with parameter $\alpha$; and the disease spreads within the population is modelled by a Poisson process with a rate $\lambda_{I}$. $\lambda_{I}=\beta I(1-\frac{I}{M}) $ is similar to the instantaneous rate in the logistic population growth model. The analysis is focused on the disease outbreak, where the reproduction number $R=\frac{\beta}{\alpha} $ is greater than one. As methodology, we use both numerical and analytical approaches. The analysis relies on the stationary distribution for Birth and Death Markov process. The numerical approach creates sample path simulations into order show the infected size dynamics, and the relationship between infected size and $R$. As $M$ becomes large, some stable statistical characteristics of the infected size distribution can be deduced. And the infected size is shown analytically to follow a normal distribution with mean $(1-\frac{1}{R}) M$ and Variance $\frac{M}{R} $.
Impact of asymptomatic COVID-19 carriers on pandemic policy outcomes
Authors: Weijie Pang, Hassan Chehaitli, T. R. Hurd
Date: 2021-02-17 00:00:00

This paper provides a mathematical model to show that the incorrect estimation of r, the fraction of asymptomatic COVID-19 carriers in the general population, can account for much of the world's failure to contain the pandemic in its early phases. The SE(A+O)R model with infectives separated into asymptomatic and ordinary carriers, supplemented by a model of the data generation process, is calibrated to standard datasets for several countries. It is shown that certain fundamental parameters, notably r, are unidentifiable with this data. A number of potential types of policy intervention are analyzed. It is found that the lack of parameter identifiability implies that only some, but not all, potential policy interventions can be correctly predicted. In an example representing Italy in March 2020, a hypothetical optimal policy of isolating confirmed cases that aims to reduce the basic reproduction number of the outbreak to R0 = 0.8 assuming r = 10%, only achieves R0 = 1.4 if it turns out that r = 40%.
Where to locate COVID-19 mass vaccination facilities?
Authors: Dimitris Bertsimas, Vassilis Digalakis Jr., Alexander Jacquillat, Michael Lingzhi Li, Alessandro Previero
Date: 2021-02-15 00:00:00
Tasks: Fairness

The outbreak of COVID-19 led to a record-breaking race to develop a vaccine. However, the limited vaccine capacity creates another massive challenge: how to distribute vaccines to mitigate the near-end impact of the pandemic? In the United States in particular, the new Biden administration is launching mass vaccination sites across the country, raising the obvious question of where to locate these clinics to maximize the effectiveness of the vaccination campaign. This paper tackles this question with a novel data-driven approach to optimize COVID-19 vaccine distribution. We first augment a state-of-the-art epidemiological model, called DELPHI, to capture the effects of vaccinations and the variability in mortality rates across age groups. We then integrate this predictive model into a prescriptive model to optimize the location of vaccination sites and subsequent vaccine allocation. The model is formulated as a bilinear, non-convex optimization model. To solve it, we propose a coordinate descent algorithm that iterates between optimizing vaccine distribution and simulating the dynamics of the pandemic. As compared to benchmarks based on demographic and epidemiological information, the proposed optimization approach increases the effectiveness of the vaccination campaign by an estimated $20\%$, saving an extra $4000$ extra lives in the United States over a three-month period. The proposed solution achieves critical fairness objectives -- by reducing the death toll of the pandemic in several states without hurting others -- and is highly robust to uncertainties and forecast errors -- by achieving similar benefits under a vast range of perturbations.
Assessing the spatio-temporal spread of COVID-19 via compartmental models with diffusion in Italy, USA, and Brazil
Authors: Malú Grave, Alex Viguerie, Gabriel F. Barros, Alessandro Reali, Alvaro L. G. A. Coutinho
Date: 2021-02-14 00:00:00
Tasks: valid

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.
A fractional-order compartmental model for predicting the spread of the Covid-19 pandemic
Authors: Toheeb A. Biala, Abdul Q. Khaliq
Date: 2020-07-08 00:00:00

We propose a time-fractional compartmental model (SEI$_A$I$_S$HRD) comprising of the susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized, recovered and dead population for the Covid-19 pandemic. We study the properties and dynamics of the proposed model. The conditions under which the disease-free and endemic equilibrium points are asymptotically stable are discussed. Furthermore, we study the sensitivity of the parameters and use the data from Tennessee state (as a case study) to discuss identifiability of the parameters of the model. The non-negative parameters in the model are obtained by solving inverse problems with empirical data from California, Florida, Georgia, Maryland, Tennessee, Texas, Washington and Wisconsin. The basic reproduction number is seen to be slightly above the critical value of one suggesting that stricter measures such as the use of face-masks, social distancing, contact tracing, and even longer stay-at-home orders need to be enforced in order to mitigate the spread of the virus. As stay-at-home orders are rescinded in some of these states, we see that the number of cases began to increase almost immediately and may continue to rise until the end of the year 2020 unless stricter measures are taken.
COVID-19 Heterogeneity in Islands Chain Environment
Authors: Monique Chyba, Alice Koniges, Prateek Kunwar, Winnie Lau, Yuriy Mileyko, Alan Tong
Date: 2021-02-12 00:00:00

As 2021 dawns, the COVID-19 pandemic is still raging strongly as vaccines finally appear and hopes for a return to normalcy start to materialize. There is much to be learned from the pandemic's first year data that will likely remain applicable to future epidemics and possible pandemics. With only minor variants in virus strain, countries across the globe have suffered roughly the same pandemic by first glance, yet few locations exhibit the same patterns of viral spread, growth, and control as the state of Hawai'i. In this paper, we examine the data and compare the COVID-19 spread statistics between the counties of Hawai'i as well as examine several locations with similar properties to Hawai'i.
Sex as information processing: optimality and evolution
Authors: Anton S Zadorin, Olivier Rivoire
Date: 2021-02-10 00:00:00

The long-term growth rate of populations in varying environments quantifies the evolutionary value of processing the information that biological individuals inherit from their ancestors and acquire from their environment. Previous models were limited to asexual reproduction with inherited information coming from a single parent with no recombination. We present a general extension to sexual reproduction and an analytical solution for a particular but important case, the infinitesimal model of quantitative genetics which assumes traits to be normally distributed. We study with this model the conditions under which sexual reproduction is advantageous and can evolve in the context of autocorrelated or directionally varying environments, mutational biases, spatial heterogeneities and phenotypic plasticity. Our results generalize and unify previous analyses. We also examine the proposal made by Geodakyan that the presence of two phenotypically distinct sexes permits an optimal adaptation to varying environments. We verify that conditions exists where sexual dimorphism is adaptive but find that its evolutionary value does not generally compensate for the two-fold cost of males.
Fitting stochastic predator-prey models using both population density and kill rate data
Authors: Frederic Barraquand, Olivier Gimenez
Date: 2019-04-03 00:00:00
Tasks: Time Series, Time Series Analysis

Most mechanistic predator-prey modelling has involved either parameterization from process rate data or inverse modelling. Here, we take a median road: we aim at identifying the potential benefits of combining datasets, when both population growth and predation processes are viewed as stochastic. We fit a discrete-time, stochastic predator-prey model of the Leslie type to simulated time series of densities and kill rate data. Our model has both environmental stochasticity in the growth rates and interaction stochasticity, i.e., a stochastic functional response. We examine what the kill rate data brings to the quality of the estimates, and whether estimation is possible (for various time series lengths) solely with time series of population counts or biomass data. Both Bayesian and frequentist estimation are performed, providing multiple ways to check model identifiability. The Fisher Information Matrix suggests that models with and without kill rate data are all identifiable, although correlations remain between parameters that belong to the same functional form. However, our results show that if the attractor is a fixed point in the absence of stochasticity, identifying parameters in practice requires kill rate data as a complement to the time series of population densities, due to the relatively flat likelihood. Only noisy limit cycle attractors can be identified directly from population count data (as in inverse modelling), although even in this case, adding kill rate data - including in small amounts - can make the estimates much more precise. Overall, we show that under process stochasticity in interaction rates, interaction data might be essential to obtain identifiable dynamical models for multiple species. These results may extend to other biotic interactions than predation, for which similar models combining interaction rates and population counts could be developed.
Modeling the process of speciation using a multi-scale framework including error estimates
Authors: Mats K. Brun, Elyes Ahmed, Jan Martin Nordbotten, Nils Christian Stenseth
Date: 2021-02-09 00:00:00

This paper concerns the modeling and numerical simulation of the process of speciation. In particular, given conditions for which one or more speciation events within an ecosystem occur, our aim is to develop the necessary modeling and simulation tools. Care is also taken to establish a solid mathematical foundation on which our modeling framework is built. This is the subject of the first half of the paper. The second half is devoted to developing a multi-scale framework for eco-evolutionary modeling, where the relevant scales are that of species and individual/population, respectively. Hence, a system of interacting species can be described at the species level, while for branching species a population level description is necessary. Our multi-scale framework thus consists of coupling the species and population level models where speciation events are detected in advance and then resolved at the population scale until the branching is complete. Moreover, since the population level model is formulated as a PDE, we first establish the well-posedness in the time-discrete setting, and then derive the a posteriori error estimates which provides a fully computable upper bound on an energy-type error, including also for the case of general smooth distributions (which will be useful for the detection of speciation events). Several numerical tests validate our framework in practice.
Bioluminescence modeling for deep sea experiments
Authors: Stephan Meighen-Berger, Li Ruohan, Golo Wimmer
Date: 2021-02-09 00:00:00
Tasks: Time Series, Time Series Analysis

We develop a modeling framework for bioluminescence light found in the deep sea near neutrino telescopes by combining a hydrodynamic model with a stochastic one. The bioluminescence is caused by organisms when exposed to a non-constant water flow, such as past the neutrino telescopes. We model the flow using the incompressible Navier-Stokes equations for Reynolds numbers between 4000 and 23000. The discretization relies on a finite element method which includes upwind-stabilization for the velocity field. On top of the flow model, we simulate a population of random microscopic organisms. Their movement and emission are stochastic processes which we model using Monte Carlo methods. We observe unique time-series for the photon counts depending on the flow velocity and detector specifications. This opens up the possibility of categorizing organisms using neutrino detectors. We show that the average light-yield and pulse shapes require precise flow modeling, while the emission timing is chaotic. From this we construct a fast modeling scheme, requiring only a subset of computationally expensive flow and population modeling.
A survey of the monotonicity and non-contradiction of consensus methods and supertree methods
Authors: Mareike Fischer, Michael Hendriksen
Date: 2021-02-08 00:00:00

In a recent study, Bryant, Francis and Steel investigated the concept of \enquote{future-proofing} consensus methods in phylogenetics. That is, they investigated if such methods can be robust against the introduction of additional data like added trees or new species. In the present manuscript, we analyze consensus methods under a different aspect of introducing new data, namely concerning the discovery of new clades. In evolutionary biology, often formerly unresolved clades get resolved by refined reconstruction methods or new genetic data analyses. In our manuscript we investigate which properties of consensus methods can guarantee that such new insights do not disagree with previously found consensus trees, but merely refine them, a property termed \emph{monotonicity}. Along the lines of analyzing monotonicity, we also study two {established} supertree methods, namely Matrix Representation with Parsimony (MRP) and Matrix Representation with Compatibility (MRC), which have also been suggested as consensus methods in the literature. While we (just like Bryant, Francis and Steel in their recent study) unfortunately have to conclude some negative answers concerning general consensus methods, we also state some relevant and positive results concerning the majority rule ($\mathtt{MR}$) and strict consensus methods, which are amongst the most frequently used consensus methods. Moreover, we show that there exist infinitely many consensus methods which are monotonic and have some other desirable properties. \textbf{Keywords:} consensus tree, phylogenetics, majority rule, tree refinement, matrix representation with parsimony \textbf{MSC:} C92B05, 05C05
Robust and optimal predictive control of the COVID-19 outbreak
Authors: Johannes Köhler, Lukas Schwenkel, Anne Koch, Julian Berberich, Patricia Pauli, Frank Allgöwer
Date: 2020-05-07 00:00:00
Tasks: Model Predictive Control

We investigate adaptive strategies to robustly and optimally control the COVID-19 pandemic via social distancing measures based on the example of Germany. Our goal is to minimize the number of fatalities over the course of two years without inducing excessive social costs. We consider a tailored model of the German COVID-19 outbreak with different parameter sets to design and validate our approach. Our analysis reveals that an open-loop optimal control policy can significantly decrease the number of fatalities when compared to simpler policies under the assumption of exact model knowledge. In a more realistic scenario with uncertain data and model mismatch, a feedback strategy that updates the policy weekly using model predictive control (MPC) leads to a reliable performance, even when applied to a validation model with deviant parameters. On top of that, we propose a robust MPC-based feedback policy using interval arithmetic that adapts the social distancing measures cautiously and safely, thus leading to a minimum number of fatalities even if measurements are inaccurate and the infection rates cannot be precisely specified by social distancing. Our theoretical findings support various recent studies by showing that 1) adaptive feedback strategies are required to reliably contain the COVID-19 outbreak, 2) well-designed policies can significantly reduce the number of fatalities compared to simpler ones while keeping the amount of social distancing measures on the same level, and 3) imposing stronger social distancing measures early on is more effective and cheaper in the long run than opening up too soon and restoring stricter measures at a later time.
Reconstructing large networks with time-varying interactions
Authors: Chun-Wei Chang, Takeshi Miki, Masayuki Ushio, Hsiao-Pei Lu, Fuh-Kwo Shiah, Chih-hao Hsieh
Date: 2021-02-08 00:00:00
Tasks: Time Series, Time Series Analysis

Reconstructing interactions from observational data is a critical need for investigating natural biological networks, wherein network dimensionality (i.e. number of interacting components) is usually high and interactions are time-varying. These pose a challenge to existing methods that can quantify only small interaction networks or assume static interactions under steady state. Here, we proposed a novel approach to reconstruct high-dimensional, time-varying interaction networks using empirical time series. This method, named "multiview distance regularized S-map", generalized the state space reconstruction to accommodate high dimensionality and overcome difficulties in quantifying massive interactions with limited data. When we evaluated this method using the time series generated from a large theoretical model involving hundreds of interacting species, estimated interaction strengths were in good agreement with theoretical expectations. As a result, reconstructed networks preserved important topological properties, such as centrality, strength distribution and derived stability measures. Moreover, our method effectively forecasted the dynamic behavior of network nodes. Applying this method to a natural bacterial community helped identify keystone species from the interaction network and revealed the mechanisms governing the dynamical stability of bacterial community. Our method overcame the challenge of high dimensionality and disentangled complex time-varying interactions in large natural dynamical systems.
Metastable states in plateaus and multi-wave epidemic dynamics of Covid-19 spreading in Italy
Authors: Gaetano Campi, Maria Vittoria Mazziotti, Antonio Valletta, Giampietro Ravagnan, Augusto Marcelli, Andrea Perali, Antonio Bianconi
Date: 2021-02-07 00:00:00

The control of Covid 19 epidemics by public health policy in Italy during the first and the second epidemic waves has been driven by using reproductive number Rt(t) to identify the supercritical (percolative), the subcritical (arrested), separated by the critical regime. Here we show that to quantify the Covid-19 spreading rate with containment measures (CSRwCM) there is a need of a 3D expanded parameter space phase diagram built by the combination of Rt(t) and doubling time Td(t). In this space we identify the dynamics of the Covid-19 dynamics Italy and its administrative Regions. The supercritical regime is mathematically characterized by i) the power law of Td vs. [Rt(t)-1] and ii) the exponential behaviour of Td vs. time, either in the first and in the second wave. The novel 3D phase diagram shows clearly metastable states appearing before and after the second wave critical regime. for loosening quarantine and tracing of actives cases. The metastable states are precursors of the abrupt onset of a next nascent wave supercritical regime. This dynamic description allows epidemics predictions needed by policymakers to activate non-pharmaceutical interventions (NPIs), a key issue for avoiding economical losses, reduce fatalities and avoid new virus variant during vaccination campaign
Evolution of populations with strategy-dependent time delays
Authors: Jacek Miȩkisz, Marek Bodnar
Date: 2021-02-07 00:00:00

We study effects of strategy-dependent time delays on equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we report a novel behavior. We show that microscopic models of evolutionary games with strategy-dependent time delays lead to a new type of replicator dynamics. It describes the time evolution of fractions of the population playing given strategies and the size of the population. Unlike in all previous models, stationary states of such dynamics depend continuously on time delays. We show that in games with an interior stationary state (a globally asymptotically stable equilibrium in the standard replicator dynamics), at certain time delays, it may disappear or there may appear another interior stationary state. In the Prisoner's Dilemma game, for time delays of cooperation smaller than time delays of defection, there appears an ustable interior equilibrium and therefore for some initial conditions, the population converges to the homogeneous state with just cooperators.
Dynamic maximum entropy provides accurate approximation of structured population dynamics
Authors: K. Bodova, E. Szep, N. H. Barton
Date: 2021-02-06 00:00:00

Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy and a quasi-stationary approximation. This allows us to reduce stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to a simpler low-dimensional deterministic dynamics, without the need to track microscopic details. Although the method has been previously applied to a few (rather complicated) applications in population genetics, our main goal here is to explain and to better understand how the method works. We demonstrate the usefulness of the method for two widely studied stochastic problems, highlighting its accuracy in capturing important macroscopic quantities even in rapidly changing non-stationary conditions. For the Ornstein-Uhlenbeck process, the method recovers the exact dynamics whilst for a stochastic island model with migration from other habitats, the approximation retains high macroscopic accuracy under a wide range of scenarios for a dynamic environment.