Mathematics

Mathematical model, analysis and simulations of the COVID-19 pandemic with variable infection rate: Application to South Korea

Speaker: 
Meir Shillor
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

The talk describes a substantial extension of the Middle East Respiratory Syndrome (MERS) model constructed, analyzed and simulated in Al-Asuoad et. al. BIOMATH 5 (2016)1, Al-Asuoad, Oakland University Dissertation (2017), and Al-Asuoad and Shillor, BIOMATH 7(1)(2018)2 to the case of the current COVID-19 Respiratory Syndrome pandemic that is sweeping the globe. It is caused by the new SARS-CoV-2 coronavirus that has been identified in December 2019 and since then outbreaks have been reported in all parts of the world. To help predict the dynamics and possible controls of the pandemic we developed a mathematical model for the pandemic. The model has a compartmental structure similar but more complex to the SARS and MERS models. It is a coupled system of nonlinear ordinary differential equations (ODEs) and a differential inclusion for the contact rate parameter. The talk will describe the model in detail, mention some of its analysis, and describe our computer simulations of the pandemic in South Korea. The main modeling novelties are in taking into account the shelter-in-place directives, the rates at which the populations obey them and the observed changes in the infectiveness of ‘contact number’ of the SARS-CoV-2 virus. The model predictions are fitted to some of the data from the outbreak in South Korea. Since the DFE (in South Korea) is found to be asymptotically stable, the pandemic will eventually die out (as long as some control measures remain in place). And, indeed, the model simulations show that the COVID-19 will in the near future be contained. However, the containment time and the severity of the outbreak depend crucially on the contact coefficients and the isolation or shelter-in-place rate constant. The simulations show that when randomness is added to the model coefficients the model captures the pandemic dynamics very well. Finally, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. It is general and will be used to analyze outbreaks in other parts of the world.

*with Aycil Cesmelioglu and Anna M. Spagnuolo

1 http://dx.doi.org /10.11145/j.biomath.2016.12.141
2 http://dx.doi.org/10.11145/j.biomath.2018.02.277

Class: 

Scenario tree and adaptive decision making on optimal type and timing for intervention and social-economic activity changes

Speaker: 
MIchael Chen
Kyeongah Nah
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

We assess Ontario’s reopening plans, taking into account the healthcare system capacity and uncertainties in contact rates during different reopening phases. Using stochastic programming and a disease transmission model, we find the optimal timing for each reopening phase that maximizes the relaxation of social contacts under uncertainties, while not overwhelming the health system capacity by an expected arrival time of a SARS-CoV-2 vaccine/drug.

* Written with Michael Chen and LIAM De-escalation Group

Class: 

Law of mass action and saturation in SIR model with applications to coronavirus

Speaker: 
Theodore Kolokolnikov
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

It is common in SIR models to assume that the infection rate is proportional to the product S*I of susceptible and infected individuals. This form is motivated by the law of mass action from chemistry. While this assumption works at the onset of the outbreak, it needs to be modified at higher rates such as seen currently in much of the world (as of June 2020). We propose a physics-based model which leads to a simple saturation formula based on first principles incorporating the spread radius and population density. We then apply this modified SIR model to coronavirus and show that it fits much better than the ``classical'' law of mass action.

Class: 

CAIMS - PIMS Coronavirus Modelling Conference - Panel

Speaker: 
Penelope Morel
Adrianne Jenner
Jane Heffernan
Wei Dai
Rohit Rao
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
Abstract: 

A panel session was heard after the morning session of the third day of this conference. The panelists were the speakers from the 4 preceeding talks.

  1. The immune response to SARS-CoV-2: Friend or Foe? - Penelope Morel
  2. Modelling the systemic and tissue-level immune response to SARS-CoV-2 - Adrianne Jenner
  3. Models for immune system interaction and evolution - Jane Heffernan
  4. A Quantitative Systems Pharmacology Model of the Immune Response to SARS-COV-2 - Wei Dai, Rohit Rao
Class: 

A Quantitative Systems Pharmacology Model of the Immune Response to SARS-COV-2

Speaker: 
Wei Dai
Rohit Rao
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

Rapid development of a QSP model to support novel COVID-19 therapies. We intend to publish this model quickly to encourage community feedback. The simulated dynamics of immune response are modeled by describing viral activation of innate and adaptive immune processes involving both pro-inflammatory mediators regulating viral clearance and cell damage (e.g. neutrophils and cytotoxic lymphocytes) as well as counter-regulatory immune suppressive mediators (e.g. Treg cells and IL-10).

Class: 

Models for immune system interaction and evolution

Speaker: 
Jane Heffernan
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

We have developed mathematical models to study SARS-CoV-2 pathogen evolution probabilities, and immunization effectiveness. In this talk, I will provide an overview of our models, and will discuss some preliminary results.

Class: 

Modelling the systemic and tissue-level immune response to SARS-CoV-2

Speaker: 
Adrianne Jenner
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

The primary distinction between severe and mild COVID-19 infections is the immune response. Disease severity and fatality has been observed to correlate with lymphopenia (low blood lymphocyte count) and increased levels of inflammatory cytokines and IL-6 (cytokine storm), damaging dysregulated macrophage responses, and T cell exhaustion due to limited recruitment. The exact mechanism driving the dynamics that ultimately result in severe COVID-19 manifestation remain unclear. Over the past two months, we have been working on developing tissue- and systemic-level models of the immune response to SARS-CoV-2 infection with the goal of pinpointing what may be causing dysregulated immune dynamics in severe cases. At the tissue level, we been working as part of an international collaboration to build a computational framework to study SARS-CoV-2 in the tissues. This platform is based upon PhysiCell, an open-source computational cell-based software. With this model, we have been investigating how the level of pro-inflammatory cytokines influence immune cell recruitment into the infected tissue and how this correlates with tissue damage. In parallel, we have constructed a systemic, within-host delay-differential equation model that accounts for the interactions between immune cell subsets, cytokines, lung tissue, and virus to help understand differential responses in COVID-19. While this work is still ongoing, this talk will address how a variety of mathematical and computational techniques contribute to the ongoing study of SARS-CoV-2 infections, helping to increase our understanding of COVID-19 severity.

* with Sofia Alfonso (McGill University), Rosemary Aogo (University of Tennessee Health Science Center), Courtney Davis (Pepperdine University), Amber M. Smith (University of Tennessee Health Science Center), Morgan Craig (Université de Montréal, CHU Sainte-Justine Research Centre)

Class: 

The immune response to SARS-CoV-2: Friend or Foe?

Speaker: 
Penelope Morel
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

The novel SARS-CoV-2 coronavirus is responsible for worldwide pandemic that has infected over 8 million people resulting in close to 500,000 deaths. The immune response to SARS-CoV-2 involves both innate and adaptive responses and it appears that the timing and magnitude of these responses are important factors in determining the outcome of the infection. For the vast majority of those infected by SARS-CovV-2 the clinical course is mild, with a significant proportion of individuals experiencing asymptomatic infection. In mild cases, it appears that classic anti- viral immunity, manifested by early type 1 interferon production, virus-specific CD8 T cells and the generation of neutralizing antibodies, is responsible for rapid viral clearance. However, the picture is very different for the 10% of infected individuals who develop serious disease, which can lead to respiratory failure, multi-organ failure and death. This is associated with a hyperinflammatory state, with high levels of circulating cytokines, and a failure of the adaptive immune response. New data are emerging concerning the factors, both genetic and environmental, that determine the clinical outcome of disease. In this talk we will examine the host and viral factors that lead either to rapid viral clearance or to severe clinical disease. Deeper understanding of the immune response to SARS-CoV-2 will lead to the development of novel therapeutics that can be tested in a modeling framework.

Class: 

Calibration of time varying contact compartmental models of SARS-COVID-19

Speaker: 
Mark Lowerison
Date: 
Tue, Jun 23, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

We present an age stratified SEIR model of COVID 19 accounting for mitigated social contacts. With this model we explore a series of relaxation and return to normal scenarios, in terms of health system burden.

Class: 

Modelling future biomedical interventions in the COVID-19 epidemic

Speaker: 
Simon de Montigny
Date: 
Tue, Jun 23, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

To date, intervention modelling in support of the COVID-19 public health response has focused on non-pharmaceutical interventions. With biomedical tools undergoing clinical trials, it is the moment to think ahead and assess how future interventions, based on these likely imperfect tools, could be used to control the COVID-19 epidemic and allow some de-escalation of current mitigation strategies. In this talk, we will discuss our preliminary work on antibody testing and vaccine interventions in a COVID-19 transmission model based on differential equations.

Class: 

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