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Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 9853-9886. doi: 10.3934/mbe.2022459
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The COVID-19 pandemic as inspiration to reconsider epidemic models: A novel approach to spatially homogeneous epidemic spread modeling

  • 1.
    Laboratory of Chemical and Environmental Technology, Department of Chemistry, Aristotle University of Thessaloniki, 54 124 Thessaloniki, 54124, Greece
  • 2.
    Laboratory of Environmental Engineering & Planning, Department of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
  • 3.
    Infectious Diseases Unit and 3rd Department of Pediatrics, Aristotle University School of Health Sciences, Hippokration Hospital, Thessaloniki, 54642, Greece
  • 4.
    Faculty of Veterinary Medicine, School of Health Sciences, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
  • 5.
    Department of Microbiology, Medical School, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
  • 6.
    Department of Haematology, First Department of Internal Medicine, Faculty of Medicine, AHEPA General Hospital, Aristotle University of Thessaloniki, Thessaloniki, 54636, Greece
  • 7.
    School of Spatial Planning and Development, Faculty of Engineering, Aristotle University of Thessaloniki, 54124, Greece
  • 8.
    National Public Health Organization, Athens, Greece
  • 9.
    European University Cyprus, Nicosia, Cyprus
  • 10.
    National and Kapodistrian University of Athens, Athens, Greece
  • 11.
    Department of Environmental Health, Directory of Epidemiology and Prevention of Non-Communicable Diseases and Injuries, National Public Health Organization, Athens, Greece
  • Received: 05 May 2022 Revised: 29 June 2022 Accepted: 30 June 2022 Published: 11 July 2022

  • 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.

    Citation: Margaritis Kostoglou, Thodoris Karapantsios, Maria Petala, Emmanuel Roilides, Chrysostomos I. Dovas, Anna Papa, Simeon Metallidis, Efstratios Stylianidis, Theodoros Lytras, Dimitrios Paraskevis, Anastasia Koutsolioutsou-Benaki, Georgios Panagiotakopoulos, Sotirios Tsiodras, Nikolaos Papaioannou. The COVID-19 pandemic as inspiration to reconsider epidemic models: A novel approach to spatially homogeneous epidemic spread modeling[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 9853-9886. doi: 10.3934/mbe.2022459

    Related Papers:

  • 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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