Mathematics

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: 

A branching process with contact tracing

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

I will look at a simple theoretical model of a standard branching process with branchers removed by a contact tracing procedure. The talk will identify the parameter range in which the contact tracing is able to make the process sub- critical.

Class: 

Modelling the impact of asymptomatic individuals

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

We designed a simple SEIR-like model including asymptomatic individuals and we explore a wide grid of parameters related to asymptomatic rate and infectiousness.

Class: 

A SEIR-like model with a time-dependent contagion factor describes the dynamics of the Covid-19 pandemic

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

We show how a simple deterministic epidemic model without spatial structure can reproduce the evolution of confirmed Covid-19 case numbers in diverse countries and Brazilian states through use of a time-dependent contagion factor, beta(t). One expects that this function provides a link between the growth rate and mitigation policies. The model inserts a state A (presymptomatic) between states E (exposed) and I (infected) in the usual SEIR model, as well as distinguishing between confirmed and unconfirmed infected. With transition rates fixed at literature values, we vary the four free parameters in beta(t) to obtain a good description of time series of the cumulative number of confirmed cases. We then analyze the relation between changes in the contagion factor, as inferred from the time- series analysis, and mobility indexes based on cell-phone data.

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Localized outbreaks in S-I-R model with diffusion

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

We investigate a SIRS epidemic model with spatial diffusion and nonlinear incidence rates. We show that for small diffusion rate of the infected class D_I, the infected population tends to be highly localized at certain points inside the domain, forming K spikes. We then study three distinct destabilization mechanisms, as well as a transition from localized spikes to plateau solutions. Two of the instabilities are due to coarsening (spike death) and self-replication (spike birth), and have well-known analogues in other reaction-diffusion systems such as the Schnakenberg model. The third transition is when a single spike becomes unstable and moves to the boundary. This happens when the diffusion of the recovered class, DR becomes sufficiently small. In all cases, the stability thresholds are computed asymptotically and are verified by numerical experiments. We also show that the spike solution can transit into a plateau-type solution when the diffusion rates of recovered and susceptible class are sufficiently small. Implications for disease spread and control through quarantine are discussed.

Class: 

Modelling evolutionary epidemiology of COVID-19

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

Evolutionary epidemiological models illustrate how selection might act on SARS-CoV-2. Considering the limited data, selection favors increased transmission, longer pre-symptomatic periods, fewer asymptomatic cases, and lower disease severity. Viral mutations are expected to affect combinations of these traits, however, making it challenging to predict the direction and disease impact of evolution.

Class: 

In-host Modelling of COVID-19 in Humans

Speaker: 
Esteban Abelardo Hernandez Vargas
Date: 
Tue, Jun 23, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat for human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. In this work, different mathematical models are proposed to represent SARS-CoV-2 dynamics in infected patients. Considering different starting times of infection, parameters sets that represent infectivity of SARS-CoV-2 are computed and compared with other viral infections that can also cause pandemics. Based on the target cell limited model, SARS-CoV-2 infecting time between susceptible cells is much slower than those reported for Ebola virus infection (about 3 times slower) and influenza infection (60 times slower). The within-host reproductive number for SARS-CoV-2 is consistent to the values of influenza infection (1.7-5.35). The best model to fit the data was including immune cell response, which suggests a slow immune response peaking between 5 to 10 days post onset of symptoms. The model with eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, both, the target cell model and the model with immune responses, predict that SARS-CoV-2 may replicate very slowly in the first days after infection, and it could be below detection levels during the first 4 days post infection. A quantitative comprehension of SARS-CoV-2 dynamics and the estimation of standard parameters of viral infections is the key contribution of this pioneering work. This work can serve for future evaluation of the potential drugs with different methods of action to inhibit SARS-CoV-2.

Class: 

Mechanistic modeling of the SARS-CoV-2 and immune system interplay unravels design principles for diverse clinicopathological outcomes

Speaker: 
Mohit Kumar Jolly
Date: 
Tue, Jun 23, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

The disease caused by SARS-CoV-2 is a global pandemic that threatens to bring long-term changes worldwide. Approximately 80% of infected patients are asymptomatic or have mild symptoms such as fever or cough, while rest of the patients have varying degrees of severity of symptoms, with 3-4% mortality rate. Severe symptoms such as pneumonia and Acute Respiratory Distress Syndrome can be caused by tissue damage mostly due to aggravated and unresolved innate and adaptive immune response, often resulting from a cytokine storm. However, the mechanistic underpinnings of such responses remain elusive, with an incomplete understanding of how an intricate interplay among infected cells and cells of innate and adaptive immune system can lead to such diverse clinicopathological outcomes. Here, we use a dynamical systems approach to dissect the emergent nonlinear intra-host dynamics among virally infected cells, the immune response to it and the consequent immunopathology. By mechanistic analysis of cell- cell interactions, we have identified key parameters affecting the diverse clinical phenotypes associated with COVID- 19. This minimalistic yet rigorous model can explain the various phenotypes observed across the clinical spectrum of COVID-19, various co-morbidity risk factors such as age and obesity, and the effect of antiviral drugs on different phenotypes. It also reveals how a fine-tuned balance of infected cell killing and resolution of inflammation can lead to infection clearance, while disruptions can drive different severe phenotypes. These results will help further the case of rational selection of drug combinations that can effectively balance viral clearance and minimize tissue damage.

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