1
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Drossinos Y, Stilianakis NI. On modelling airborne infection risk. ROYAL SOCIETY OPEN SCIENCE 2024; 11:231976. [PMID: 39050731 PMCID: PMC11265909 DOI: 10.1098/rsos.231976] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Revised: 05/28/2024] [Accepted: 06/11/2024] [Indexed: 07/27/2024]
Abstract
Airborne infection risk analysis is usually performed for enclosed spaces where susceptible individuals are exposed to infectious airborne respiratory droplets by inhalation. It is usually based on exponential, dose-response models of which a widely used variant is the Wells-Riley (WR) model. We revisit this infection-risk estimate and extend it to the population level. We use an epidemiological model where the mode of pathogen transmission, airborne or contact, is explicitly considered. We illustrate the link between epidemiological models and the WR and the Gammaitoni and Nucci models. We argue that airborne infection quanta are, up to an overall density, airborne infectious respiratory droplets modified by a parameter that depends on biological properties of the pathogen, physical properties of the droplet and behavioural properties of the individual. We calculate the time-dependent risk of being infected for two scenarios. We show how the epidemic infection risk depends on the viral latent period and the event time, the time infection occurs. Infection risk follows the dynamics of the infected population. As the latent period decreases, infection risk increases. The longer a susceptible is present in the epidemic, the higher its risk of infection for equal exposure time to the pathogen is.
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Affiliation(s)
- Yannis Drossinos
- Thermal Hydraulics & Multiphase Flow Laboratory, Institute of Nuclear & Radiological Sciences and Technology, Energy & Safety, National Centre for Scientific Research “Demokritos”, Agia Paraskevi15314, Greece
| | - Nikolaos I. Stilianakis
- Joint Research Centre (JRC), European Commission, Ispra, VA21027, Italy
- Department of Biometry and Epidemiology, University of Erlangen-Nuremberg, Erlangen, Germany
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2
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Nitzsche C, Simm S. Agent-based modeling to estimate the impact of lockdown scenarios and events on a pandemic exemplified on SARS-CoV-2. Sci Rep 2024; 14:13391. [PMID: 38862580 PMCID: PMC11167020 DOI: 10.1038/s41598-024-63795-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 06/03/2024] [Indexed: 06/13/2024] Open
Abstract
In actual pandemic situations like COVID-19, it is important to understand the influence of single mitigation measures as well as combinations to create most dynamic impact for lockdown scenarios. Therefore we created an agent-based model (ABM) to simulate the spread of SARS-CoV-2 in an abstract city model with several types of places and agents. In comparison to infection numbers in Germany our ABM could be shown to behave similarly during the first wave. In our model, we implemented the possibility to test the effectiveness of mitigation measures and lockdown scenarios on the course of the pandemic. In this context, we focused on parameters of local events as possible mitigation measures and ran simulations, including varying size, duration, frequency and the proportion of events. The majority of changes to single event parameters, with the exception of frequency, showed only a small influence on the overall course of the pandemic. By applying different lockdown scenarios in our simulations, we could observe drastic changes in the number of infections per day. Depending on the lockdown strategy, we even observed a delayed peak in infection numbers of the second wave. As an advantage of the developed ABM, it is possible to analyze the individual risk of single agents during the pandemic. In contrast to standard or adjusted ODEs, we observed a 21% (with masks) / 48% (without masks) increased risk for single reappearing participants on local events, with a linearly increasing risk based on the length of the events.
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Affiliation(s)
- Christian Nitzsche
- University Medicine Greifswald, Institute of Bioinformatics, Greifswald, 17489, Germany
| | - Stefan Simm
- University Medicine Greifswald, Institute of Bioinformatics, Greifswald, 17489, Germany.
- Coburg University of Applied Sciences, Institute of Bioanalysis, Coburg, Germany.
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3
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Wang L, Khan AA, Ullah S, Haider N, AlQahtani SA, Saqib AB. A rigorous theoretical and numerical analysis of a nonlinear reaction-diffusion epidemic model pertaining dynamics of COVID-19. Sci Rep 2024; 14:7902. [PMID: 38570524 PMCID: PMC10991520 DOI: 10.1038/s41598-024-56469-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2023] [Accepted: 03/06/2024] [Indexed: 04/05/2024] Open
Abstract
The spatial movement of the human population from one region to another and the existence of super-spreaders are the main factors that enhanced the disease incidence. Super-spreaders refer to the individuals having transmitting ability to multiple pathogens. In this article, an epidemic model with spatial and temporal effects is formulated to analyze the impact of some preventing measures of COVID-19. The model is developed using six nonlinear partial differential equations. The infectious individuals are sub-divided into symptomatic, asymptomatic and super-spreader classes. In this study, we focused on the rigorous qualitative analysis of the reaction-diffusion model. The fundamental mathematical properties of the proposed COVID-19 epidemic model such as boundedness, positivity, and invariant region of the problem solution are derived, which ensure the validity of the proposed model. The model equilibria and its stability analysis for both local and global cases have been presented. The normalized sensitivity analysis of the model is carried out in order to observe the crucial factors in the transmission of infection. Furthermore, an efficient numerical scheme is applied to solve the proposed model and detailed simulation are performed. Based on the graphical observation, diffusion in the context of confined public gatherings is observed to significantly inhibit the spread of infection when compared to the absence of diffusion. This is especially important in scenarios where super-spreaders may play a major role in transmission. The impact of some non-pharmaceutical interventions are illustrated graphically with and without diffusion. We believe that the present investigation will be beneficial in understanding the complex dynamics and control of COVID-19 under various non-pharmaceutical interventions.
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Affiliation(s)
- Laiquan Wang
- Department of Basic Courses, Changji Vocational and Technical College, Changji, 831100, China
| | - Arshad Alam Khan
- Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan
| | - Saif Ullah
- Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan
| | - Nadeem Haider
- Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan
| | - Salman A AlQahtani
- Computer Engineering Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia
| | - Abdul Baseer Saqib
- Faculty of Education, Department of Mathematics, Nangrahar University, Nangrahar, Afghanistan.
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4
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Cuevas-Maraver J, Kevrekidis PG, Chen QY, Kevrekidis GA, Drossinos Y. Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants. Math Biosci 2024; 367:109109. [PMID: 37981262 DOI: 10.1016/j.mbs.2023.109109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Revised: 10/14/2023] [Accepted: 11/14/2023] [Indexed: 11/21/2023]
Abstract
We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant. The first one is for the delta variant, where we do not follow the dynamics of the vaccinated individuals since infections of vaccinated individuals were rare. The second one for the far more contagious omicron variant incorporates the evolution of the infections within the vaccinated cohort. We explore comparisons with available data involving two possible classes of counts, fatalities and hospitalizations. We present our results for two regions, Andalusia and Switzerland (including the Principality of Liechtenstein), where the necessary data are available. In the majority of the considered cases, the models are found to yield good agreement with the data and have a reasonable predictive capability beyond their training window, rendering them potentially useful tools for the interpretation of the COVID-19 and further pandemic waves, and for the design of intervention strategies during these waves.
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Affiliation(s)
- J Cuevas-Maraver
- Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla. Escuela Politécnica Superior, C/ Virgen de África, 7, 41011 Sevilla, Spain; Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Edificio Celestino Mutis. Avda. Reina Mercedes s/n, 41012 Sevilla, Spain.
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
| | - Q Y Chen
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
| | - G A Kevrekidis
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA; Los Alamos National Laboratory, Los Alamos, NM, USA; Mathematical Institute for Data Science, Johns Hopkins University, Baltimore MD, USA
| | - Y Drossinos
- Thermal Hydraulics & Multiphase Flow Laboratory, Institute of Nuclear & Radiological Sciences and Technology, Energy & Safety, N.C.S.R. "Demokritos", GR 15341, Agia Paraskevi, Greece
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5
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Okolie A, Müller J, Kretzschmar M. Parameter estimation for contact tracing in graph-based models. J R Soc Interface 2023; 20:20230409. [PMID: 37989228 PMCID: PMC10668870 DOI: 10.1098/rsif.2023.0409] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 11/01/2023] [Indexed: 11/23/2023] Open
Abstract
We adopt a maximum-likelihood framework to estimate parameters of a stochastic susceptible-infected-recovered (SIR) model with contact tracing on a rooted random tree. Given the number of detectees per index case, our estimator allows to determine the degree distribution of the random tree as well as the tracing probability. Since we do not discover all infectees via contact tracing, this estimation is non-trivial. To keep things simple and stable, we develop an approximation suited for realistic situations (contract tracing probability small, or the probability for the detection of index cases small). In this approximation, the only epidemiological parameter entering the estimator is R0. The estimator is tested in a simulation study and is furthermore applied to COVID-19 contact tracing data from India. The simulation study underlines the efficiency of the method. For the empirical COVID-19 data, we compare different degree distributions and perform a sensitivity analysis. We find that particularly a power-law and a negative binomial degree distribution fit the data well and that the tracing probability is rather large. The sensitivity analysis shows no strong dependency of the estimates on the reproduction number. Finally, we discuss the relevance of our findings.
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Affiliation(s)
- Augustine Okolie
- Center for Mathematical Sciences, Technische Universität München, 85748 Garching, Germany
| | - Johannes Müller
- Center for Mathematical Sciences, Technische Universität München, 85748 Garching, Germany
- Institute for Computational Biology, Helmholtz Center Munich, 85764 Neuherberg, Germany
| | - Mirjam Kretzschmar
- University Medical Center Utrecht, Utrecht University, 3584CX Utrecht, The Netherlands
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6
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Sun HC, Pei S, Wang L, Sun YY, Xu XK. The Impact of Spring Festival Travel on Epidemic Spreading in China. Viruses 2023; 15:1527. [PMID: 37515214 PMCID: PMC10384880 DOI: 10.3390/v15071527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2023] [Revised: 07/03/2023] [Accepted: 07/07/2023] [Indexed: 07/30/2023] Open
Abstract
The large population movement during the Spring Festival travel in China can considerably accelerate the spread of epidemics, especially after the relaxation of strict control measures against COVID-19. This study aims to assess the impact of population migration in Spring Festival holiday on epidemic spread under different scenarios. Using inter-city population movement data, we construct the population flow network during the non-holiday time as well as the Spring Festival holiday. We build a large-scale metapopulation model to simulate the epidemic spread among 371 Chinese cities. We analyze the impact of Spring Festival travel on the peak timing and peak magnitude nationally and in each city. Assuming an R0 (basic reproduction number) of 15 and the initial conditions as the reported COVID-19 infections on 17 December 2022, model simulations indicate that the Spring Festival travel can substantially increase the national peak magnitude of infection. The infection peaks arrive at most cities 1-4 days earlier as compared to those of the non-holiday time. While peak infections in certain large cities, such as Beijing and Shanghai, are decreased due to the massive migration of people to smaller cities during the pre-Spring Festival period, peak infections increase significantly in small- or medium-sized cities. For a less transmissible disease (R0 = 5), infection peaks in large cities are delayed until after the Spring Festival. Small- or medium-sized cities may experience a larger infection due to the large-scale population migration from metropolitan areas. The increased disease burden may impose considerable strain on the healthcare systems in these resource-limited areas. For a less transmissible disease, particular attention needs to be paid to outbreaks in large cities when people resume work after holidays.
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Affiliation(s)
- Hao-Chen Sun
- College of Computer Science and Technology, Dalian University of Technology, Dalian 116024, China; (H.-C.S.); (Y.-Y.S.)
| | - Sen Pei
- Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY 10032, USA
| | - Lin Wang
- Department of Genetics, University of Cambridge, Cambridge CB2 3EH, UK;
| | - Yuan-Yuan Sun
- College of Computer Science and Technology, Dalian University of Technology, Dalian 116024, China; (H.-C.S.); (Y.-Y.S.)
| | - Xiao-Ke Xu
- Computational Communication Research Center, Beijing Normal University, Zhuhai 519087, China
- School of Journalism and Communication, Beijing Normal University, Beijing 100875, China
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7
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Rapti Z, Cuevas-Maraver J, Kontou E, Liu S, Drossinos Y, Kevrekidis PG, Barmann M, Chen QY, Kevrekidis GA. The Role of Mobility in the Dynamics of the COVID-19 Epidemic in Andalusia. Bull Math Biol 2023; 85:54. [PMID: 37166513 PMCID: PMC10173246 DOI: 10.1007/s11538-023-01152-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Accepted: 03/28/2023] [Indexed: 05/12/2023]
Abstract
Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e., between the first and second pandemic waves). Our aim is to consider the possibility of incorporation of mobility across the province nodes focusing on mobile-phone time-dependent data, but also discussing the comparison for our case example with a gravity model, as well as with the dynamics in the absence of mobility. Our main finding is that mobility is key toward a quantitative understanding of the emergence of the second wave of the pandemic and that the most accurate way to capture it involves dynamic (rather than static) inclusion of time-dependent mobility matrices based on cell-phone data. Alternatives bearing no mobility are unable to capture the trends revealed by the data in the context of the metapopulation model considered herein.
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Affiliation(s)
- Z Rapti
- Department of Mathematics and Carl R. Woese Institute for Genomic Biology, University of Illinois Urbana-Champaign, Champaign, IL, USA.
| | - J Cuevas-Maraver
- Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla, Escuela Politécnica Superior, C/ Virgen de Africa, 7, 41011, Seville, Spain
- Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Edificio Celestino Mutis, Avda. Reina Mercedes s/n, 41012, Seville, Spain
| | - E Kontou
- Department of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, Champaign, IL, USA
| | - S Liu
- Department of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, Champaign, IL, USA
| | - Y Drossinos
- Thermal Hydraulics and Multiphase Flow Laboratory, Institute of Nuclear and Radiological Sciences and Technology, Energy and Safety, N.C.S.R. "Demokritos", 15341, Agia Paraskevi, Greece
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003-4515, USA
| | - M Barmann
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003-4515, USA
| | - Q-Y Chen
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003-4515, USA
| | - G A Kevrekidis
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, 21218, USA
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8
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Alshehri A, Ullah S. A numerical study of COVID-19 epidemic model with vaccination and diffusion. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:4643-4672. [PMID: 36896516 DOI: 10.3934/mbe.2023215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The coronavirus infectious disease (or COVID-19) is a severe respiratory illness. Although the infection incidence decreased significantly, still it remains a major panic for human health and the global economy. The spatial movement of the population from one region to another remains one of the major causes of the spread of the infection. In the literature, most of the COVID-19 models have been constructed with only temporal effects. In this paper, a vaccinated spatio-temporal COVID-19 mathematical model is developed to study the impact of vaccines and other interventions on the disease dynamics in a spatially heterogeneous environment. Initially, some of the basic mathematical properties including existence, uniqueness, positivity, and boundedness of the diffusive vaccinated models are analyzed. The model equilibria and the basic reproductive number are presented. Further, based upon the uniform and non-uniform initial conditions, the spatio-temporal COVID-19 mathematical model is solved numerically using finite difference operator-splitting scheme. Furthermore, detailed simulation results are presented in order to visualize the impact of vaccination and other model key parameters with and without diffusion on the pandemic incidence. The obtained results reveal that the suggested intervention with diffusion has a significant impact on the disease dynamics and its control.
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Affiliation(s)
- Ahmed Alshehri
- Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Saif Ullah
- Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan
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9
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Kevrekidis GA, Rapti Z, Drossinos Y, Kevrekidis PG, Barmann MA, Chen QY, Cuevas-Maraver J. Backcasting COVID-19: a physics-informed estimate for early case incidence. ROYAL SOCIETY OPEN SCIENCE 2022; 9:220329. [PMID: 36533196 PMCID: PMC9748501 DOI: 10.1098/rsos.220329] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 11/17/2022] [Indexed: 06/17/2023]
Abstract
It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embedding theorems of Whitney and Takens and use Gaussian process regression to estimate the number of cases during the first 2020 wave based on the second wave of the epidemic in several European countries, South Korea and Brazil. We assume that the second wave was more accurately monitored, even though we acknowledge that behavioural changes occurred during the pandemic and region- (or country-) specific monitoring protocols evolved. We then construct a manifold diffeomorphic to that of the implied original dynamical system, using fatalities or hospitalizations only. Finally, we restrict the diffeomorphism to the reported cases coordinate of the dynamical system. Our main finding is that in the European countries studied, the actual cases are under-reported by as much as 50%. On the other hand, in South Korea-which had a proactive mitigation approach-a far smaller discrepancy between the actual and reported cases is predicted, with an approximately 18% predicted underestimation. We believe that our backcasting framework is applicable to other epidemic outbreaks where (due to limited or poor quality data) there is uncertainty around the actual cases.
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Affiliation(s)
- G. A. Kevrekidis
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
| | - Z. Rapti
- Department of Mathematics and Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61820, USA
| | - Y. Drossinos
- European Commission, Joint Research Centre, I-21027 Ispra (VA), Italy
| | - P. G. Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
| | - M. A. Barmann
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
| | - Q. Y. Chen
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
| | - J. Cuevas-Maraver
- Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla. Escuela Politécnica Superior, C/ Virgen de África, 7, 41012 Sevilla, Spain
- Instituto de Matemáticas de la Universidad de Sevilla (IMUS). Edificio Celestino Mutis. Avda. Reina Mercedes s/n, 41012 Sevilla, Spain
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10
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Vaziry A, Kolokolnikov T, Kevrekidis PG. Modelling of spatial infection spread through heterogeneous population: from lattice to partial differential equation models. ROYAL SOCIETY OPEN SCIENCE 2022; 9:220064. [PMID: 36249333 PMCID: PMC9533003 DOI: 10.1098/rsos.220064] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 09/05/2022] [Indexed: 06/16/2023]
Abstract
We present a simple model for the spread of an infection that incorporates spatial variability in population density. Starting from first-principle considerations, we explore how a novel partial differential equation with state-dependent diffusion can be obtained. This model exhibits higher infection rates in the areas of higher population density-a feature that we argue to be consistent with epidemiological observations. The model also exhibits an infection wave, the speed of which varies with population density. In addition, we demonstrate the possibility that an infection can 'jump' (i.e. tunnel) across areas of low population density towards areas of high population density. We briefly touch upon the data reported for coronavirus spread in the Canadian province of Nova Scotia as a case example with a number of qualitatively similar features as our model. Lastly, we propose a number of generalizations of the model towards future studies.
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Affiliation(s)
- Arvin Vaziry
- Department of Mathematics and Statistics, Dalhousie University Halifax, Nova Scotia, Canada B3H3J5
| | - T. Kolokolnikov
- Department of Mathematics and Statistics, Dalhousie University Halifax, Nova Scotia, Canada B3H3J5
| | - P. G. Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA
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11
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Kostoglou M, Karapantsios T, Petala M, Roilides E, Dovas CI, Papa A, Metallidis S, Stylianidis E, Lytras T, Paraskevis D, Koutsolioutsou-Benaki A, Panagiotakopoulos G, Tsiodras S, Papaioannou N. The COVID-19 pandemic as inspiration to reconsider epidemic models: A novel approach to spatially homogeneous epidemic spread modeling. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:9853-9876. [PMID: 36031972 DOI: 10.3934/mbe.2022459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Epidemic spread models are useful tools to study the spread and the effectiveness of the interventions at a population level, to an epidemic. The workhorse of spatially homogeneous class models is the SIR-type ones comprising ordinary differential equations for the unknown state variables. The transition between different states is expressed through rate functions. Inspired by -but not restricted to- features of the COVID-19 pandemic, a new framework for modeling a disease spread is proposed. The main concept refers to the assignment of properties to each individual person as regards his response to the disease. A multidimensional distribution of these properties represents the whole population. The temporal evolution of this distribution is the only dependent variable of the problem. All other variables can be extracted by post-processing of this distribution. It is noteworthy that the new concept allows an improved consideration of vaccination modeling because it recognizes vaccination as a modifier of individuals response to the disease and not as a means for individuals to totally defeat the disease. At the heart of the new approach is an infection age model engaging a sharp cut-off. This model is analyzed in detail, and it is shown to admit self-similar solutions. A hierarchy of models based on the new approach, from a generalized one to a specific one with three dominant properties, is derived. The latter is implemented as an example and indicative results are presented and discussed. It appears that the new framework is general and versatile enough to simulate disease spread processes and to predict the evolution of several variables of the population during this spread.
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Affiliation(s)
- Margaritis Kostoglou
- Laboratory of Chemical and Environmental Technology, Department of Chemistry, Aristotle University of Thessaloniki, 54 124 Thessaloniki, 54124, Greece
| | - Thodoris Karapantsios
- Laboratory of Chemical and Environmental Technology, Department of Chemistry, Aristotle University of Thessaloniki, 54 124 Thessaloniki, 54124, Greece
| | - Maria Petala
- Laboratory of Environmental Engineering & Planning, Department of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
| | - Emmanuel Roilides
- Infectious Diseases Unit and 3rd Department of Pediatrics, Aristotle University School of Health Sciences, Hippokration Hospital, Thessaloniki, 54642, Greece
| | - Chrysostomos I Dovas
- Faculty of Veterinary Medicine, School of Health Sciences, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
| | - Anna Papa
- Department of Microbiology, Medical School, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
| | - Simeon Metallidis
- Department of Haematology, First Department of Internal Medicine, Faculty of Medicine, AHEPA General Hospital, Aristotle University of Thessaloniki, Thessaloniki, 54636, Greece
| | - Efstratios Stylianidis
- School of Spatial Planning and Development, Faculty of Engineering, Aristotle University of Thessaloniki, 54124, Greece
| | - Theodoros Lytras
- National Public Health Organization, Athens, Greece
- European University Cyprus, Nicosia, Cyprus
| | | | - Anastasia Koutsolioutsou-Benaki
- Department of Environmental Health, Directory of Epidemiology and Prevention of Non-Communicable Diseases and Injuries, National Public Health Organization, Athens, Greece
| | | | | | - Nikolaos Papaioannou
- Faculty of Veterinary Medicine, School of Health Sciences, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
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12
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Linot AJ, Graham MD. Data-driven reduced-order modeling of spatiotemporal chaos with neural ordinary differential equations. CHAOS (WOODBURY, N.Y.) 2022; 32:073110. [PMID: 35907719 DOI: 10.1063/5.0069536] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Accepted: 06/15/2022] [Indexed: 06/15/2023]
Abstract
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced-order modeling method that capitalizes on this fact by finding a coordinate representation for this manifold and then a system of ordinary differential equations (ODEs) describing the dynamics in this coordinate system. The manifold coordinates are discovered using an undercomplete autoencoder-a neural network (NN) that reduces and then expands dimension. Then, the ODE, in these coordinates, is determined by a NN using the neural ODE framework. Both of these steps only require snapshots of data to learn a model, and the data can be widely and/or unevenly spaced. Time-derivative information is not needed. We apply this framework to the Kuramoto-Sivashinsky equation for domain sizes that exhibit chaotic dynamics with again estimated manifold dimensions ranging from 8 to 28. With this system, we find that dimension reduction improves performance relative to predictions in the ambient space, where artifacts arise. Then, with the low-dimensional model, we vary the training data spacing and find excellent short- and long-time statistical recreation of the true dynamics for widely spaced data (spacing of ∼ 0.7 Lyapunov times). We end by comparing performance with various degrees of dimension reduction and find a "sweet spot" in terms of performance vs dimension.
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Affiliation(s)
- Alec J Linot
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Michael D Graham
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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Cheng Z, Wang J. Modeling epidemic flow with fluid dynamics. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:8334-8360. [PMID: 35801468 DOI: 10.3934/mbe.2022388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
In this paper, a new mathematical model based on partial differential equations is proposed to study the spatial spread of infectious diseases. The model incorporates fluid dynamics theory and represents the epidemic spread as a fluid motion generated through the interaction between the susceptible and infected hosts. At the macroscopic level, the spread of the infection is modeled as an inviscid flow described by the Euler equation. Nontrivial numerical methods from computational fluid dynamics (CFD) are applied to investigate the model. In particular, a fifth-order weighted essentially non-oscillatory (WENO) scheme is employed for the spatial discretization. As an application, this mathematical and computational framework is used in a simulation study for the COVID-19 outbreak in Wuhan, China. The simulation results match the reported data for the cumulative cases with high accuracy and generate new insight into the complex spatial dynamics of COVID-19.
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Affiliation(s)
- Ziqiang Cheng
- School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
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Chondros C, Nikolopoulos SD, Polenakis I. An integrated simulation framework for the prevention and mitigation of pandemics caused by airborne pathogens. NETWORK MODELING AND ANALYSIS IN HEALTH INFORMATICS AND BIOINFORMATICS 2022; 11:42. [PMID: 36277296 PMCID: PMC9579666 DOI: 10.1007/s13721-022-00385-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Revised: 09/24/2022] [Accepted: 09/24/2022] [Indexed: 11/07/2022]
Abstract
In this work, we developed an integrated simulation framework for pandemic prevention and mitigation of pandemics caused by airborne pathogens, incorporating three sub-models, namely the spatial model, the mobility model, and the propagation model, to create a realistic simulation environment for the evaluation of the effectiveness of different countermeasures on the epidemic dynamics. The spatial model converts images of real cities obtained from Google Maps into undirected weighted graphs that capture the spatial arrangement of the streets utilized next for the mobility of individuals. The mobility model implements a stochastic agent-based approach, developed to assign specific routes to individuals moving in the city, through the use of stochastic processes, utilizing the weights of the underlying graph to deploy shortest path algorithms. The propagation model implements both the epidemiological model and the physical substance of the transmission of an airborne pathogen (in our approach, we investigate the transmission parameters of SARS-CoV-2). The deployment of a set of countermeasures was investigated in reducing the spread of the pathogen, where, through a series of repetitive simulation experiments, we evaluated the effectiveness of each countermeasure in pandemic prevention.
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Affiliation(s)
- Christos Chondros
- Department of Computer Science and Engineering, University of Ioannina, 45100 Ioannina, Greece
| | - Stavros D. Nikolopoulos
- Department of Computer Science and Engineering, University of Ioannina, 45100 Ioannina, Greece
| | - Iosif Polenakis
- Department of Computer Science and Engineering, University of Ioannina, 45100 Ioannina, Greece
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