A mechanistic population balance model to evaluate the impact of interventions on infectious disease outbreaks: Case for COVID19

Infectious diseases can be devastating, especially when new and highly contagious, producing epidemic outbreaks that can become pandemics. Such is the case of COVID-19, the worst pandemic the world has seen in more than 100 years. Predicting the course and outcomes of such a pandemic in relation to possible interventions is crucial for societal and healthcare planning and forecasting of resource needs. In this work a deterministic model was developed, using elements from the SIR-type models, that describes individuals in a population in compartments by infection stage and age group. The model assumes a close well-mixed community with no migrations. Infection rates and clinical and epidemiological information govern the transitions between stages of the disease. The present model provides a platform to build upon and its current low complexity retains accessibility to both experts and non-experts as well as policy makers to comprehend the variables and phenomena at play. The impact of several possible interventions that have been or may be applied to slow the spread of the COVID-19 outbreak is evaluated. Key findings in our model simulation results indicate that (i) universal social isolation measures may be effective in reducing total fatalities only if they are strict and the average number of daily social interactions is reduced to very low numbers; (ii) selective isolation of only the age groups most vulnerable to the disease (i.e. older than 60) appears almost as effective in reducing total fatalities but at a much lower economic damage; (iii) the use of protective equipment (PPE) appears capable of very significantly reducing total fatalities if implemented extensively and to a high degree; (iv) extensive random testing of the population leading to infection recognition and subsequent immediate (self) isolation of the infected individuals, appears to be an ineffective intervention due to the required (unreachable with existing test sensitivities) high percentage of infection detections and the incapability to be sustained over time; (v) an increase in the number of critical care beds to directly save significant numbers of lives with a direct reduction in total final fatalities per each extra available critical care bed unit.

[1]  Xiao-Qiang Zhao,et al.  Computation of the basic reproduction numbers for reaction-diffusion epidemic models , 2023, Mathematical biosciences and engineering : MBE.

[2]  R. May,et al.  Population biology of infectious diseases: Part II , 1979, Nature.

[3]  Jean-Paul Chretien,et al.  Using “outbreak science” to strengthen the use of models during epidemics , 2019, Nature Communications.

[4]  Timothy C. Reluga,et al.  Game Theory of Social Distancing in Response to an Epidemic , 2010, PLoS Comput. Biol..

[5]  P. Klepac,et al.  Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts , 2020, The Lancet Global Health.

[6]  Lucia Russo,et al.  Mathematical modeling of infectious disease dynamics , 2013, Virulence.

[7]  Jian-ming Wang,et al.  Clinical characteristics of 24 asymptomatic infections with COVID-19 screened among close contacts in Nanjing, China , 2020, Science China Life Sciences.

[8]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[9]  P. Klepac,et al.  Early dynamics of transmission and control of COVID-19: a mathematical modelling study , 2020, The Lancet Infectious Diseases.

[10]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[11]  J. Root,et al.  Materials and strategies that work in low literacy health communication. , 1994, Public health reports.

[12]  J. Hyman,et al.  Real-time forecasts of the 2019-nCoV epidemic in China from February 5th to February 24th, 2020 , 2020, 2002.05069.

[13]  Carlos Castillo-Chavez,et al.  A simple epidemic model with surprising dynamics. , 2004, Mathematical biosciences and engineering : MBE.

[14]  G Chowell,et al.  Real-time forecasting of epidemic trajectories using computational dynamic ensembles. , 2019, Epidemics.

[15]  Alan D. Lopez,et al.  Alternative projections of mortality and disability by cause 1990–2020: Global Burden of Disease Study , 1997, The Lancet.

[16]  Alessandro Vespignani,et al.  Real-time numerical forecast of global epidemic spreading: case study of 2009 A/H1N1pdm , 2012, BMC Medicine.

[17]  L. Bettencourt,et al.  Real Time Bayesian Estimation of the Epidemic Potential of Emerging Infectious Diseases , 2008, PloS one.

[18]  M. Keeling,et al.  Modeling Infectious Diseases in Humans and Animals , 2007 .

[19]  S. Riley Large-Scale Spatial-Transmission Models of Infectious Disease , 2007, Science.

[20]  Alan D. Lopez,et al.  Regional patterns of disability-free life expectancy and disability-adjusted life expectancy: Global Burden of Disease Study , 1997, The Lancet.

[21]  Eli P. Fenichel,et al.  Adaptive human behavior in epidemiological models , 2011, Proceedings of the National Academy of Sciences.

[22]  W. Team Ebola Virus Disease in West Africa — The First 9 Months of the Epidemic and Forward Projections , 2014 .

[23]  N. Linton,et al.  Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19) , 2020, International Journal of Infectious Diseases.

[24]  Alessandro Vespignani,et al.  Assessing the International Spreading Risk Associated with the 2014 West African Ebola Outbreak , 2014, PLoS currents.

[25]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[26]  Vincenzo Capasso,et al.  Analysis of a Reaction-Diffusion System Modeling Man-Environment-Man Epidemics , 1997, SIAM J. Appl. Math..

[27]  S. Goodreau,et al.  Mathematical Modeling of Infectious Disease , 2015 .

[28]  J. Xiang,et al.  Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study , 2020, The Lancet.

[29]  Alessandro Vespignani,et al.  Modeling the spatial spread of infectious diseases: The GLobal Epidemic and Mobility computational model , 2010, J. Comput. Sci..

[30]  C. Watkins,et al.  The spread of awareness and its impact on epidemic outbreaks , 2009, Proceedings of the National Academy of Sciences.

[31]  C. Zarcadoolas,et al.  The simplicity complex: exploring simplified health messages in a complex world. , 2011, Health promotion international.

[32]  Carl A. B. Pearson,et al.  The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study , 2020, The Lancet Public Health.

[33]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[34]  N. Grassly,et al.  Mathematical models of infectious disease transmission , 2008, Nature Reviews Microbiology.

[35]  Xin-She Yang,et al.  Nature-Inspired Optimization Algorithms: Challenges and Open Problems , 2020, J. Comput. Sci..

[36]  Timothy F. Leslie,et al.  Complexity of the Basic Reproduction Number (R0) , 2019, Emerging infectious diseases.

[37]  H. McCallum,et al.  How should pathogen transmission be modelled? , 2001, Trends in ecology & evolution.

[38]  M. Hernán,et al.  Prevalence of SARS-CoV-2 in Spain (ENE-COVID): a nationwide, population-based seroepidemiological study , 2020, The Lancet.

[39]  D. Cummings,et al.  Strategies for mitigating an influenza pandemic , 2006, Nature.

[40]  Jia Li,et al.  Epidemiological Models for Mutating Pathogens , 2004, SIAM J. Appl. Math..

[41]  L. Haidari,et al.  Modelling during an emergency: the 2009 H1N1 influenza pandemic. , 2013, Clinical microbiology and infection : the official publication of the European Society of Clinical Microbiology and Infectious Diseases.

[42]  Hannah R. Meredith,et al.  The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application , 2020, Annals of Internal Medicine.

[43]  M. Keeling,et al.  Networks and epidemic models , 2005, Journal of The Royal Society Interface.

[44]  R. May,et al.  Population Biology of Infectious Diseases , 1982, Dahlem Workshop Reports.

[45]  S. Leach,et al.  Real-time epidemic forecasting for pandemic influenza , 2006, Epidemiology and Infection.

[46]  C. Whittaker,et al.  Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand , 2020 .

[47]  S. Cauchemez,et al.  Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature , 2014, BMC Infectious Diseases.

[48]  Susana Peinado,et al.  The Health Literacy Skills Framework , 2012, Journal of health communication.

[49]  F. Brauer,et al.  Mathematical Models in Population Biology and Epidemiology , 2001 .

[50]  W. Edmunds,et al.  Delaying the International Spread of Pandemic Influenza , 2006, PLoS medicine.

[51]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[52]  Alan D. Lopez,et al.  Mortality by cause for eight regions of the world: Global Burden of Disease Study , 1997, The Lancet.

[53]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[54]  D. Ramkrishna,et al.  Population balance modeling: current status and future prospects. , 2014, Annual review of chemical and biomolecular engineering.

[55]  Shigui Ruan,et al.  Dynamical behavior of an epidemic model with a nonlinear incidence rate , 2003 .

[56]  Alan D. Lopez,et al.  Global mortality, disability, and the contribution of risk factors: Global Burden of Disease Study , 1997, The Lancet.

[57]  Liangjian Hu,et al.  A Stochastic Differential Equation SIS Epidemic Model , 2011, SIAM J. Appl. Math..

[58]  Joel C Miller,et al.  Edge-based compartmental modelling for infectious disease spread , 2011, Journal of The Royal Society Interface.

[59]  E. Nsoesie,et al.  A systematic review of studies on forecasting the dynamics of influenza outbreaks , 2013, Influenza and other respiratory viruses.

[60]  Gerardo Chowell,et al.  Did Modeling Overestimate the Transmission Potential of Pandemic (H1N1-2009)? Sample Size Estimation for Post-Epidemic Seroepidemiological Studies , 2011, PloS one.

[61]  Mogens Henze,et al.  Activated sludge models ASM1, ASM2, ASM2d and ASM3 , 2015 .

[62]  S. Bhatt,et al.  Report 13: Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries , 2020 .

[63]  Hiroshi Nishiura,et al.  Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009) , 2011, Biomedical engineering online.

[64]  Tom Britton,et al.  Stochastic epidemic models: a survey. , 2009, Mathematical biosciences.

[65]  C. Viboud,et al.  Mathematical models to characterize early epidemic growth: A review. , 2016, Physics of life reviews.

[66]  Alessandro Vespignani,et al.  Spread of Zika virus in the Americas , 2017, Proceedings of the National Academy of Sciences.