Mathematics

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.

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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.

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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.

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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.

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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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The timing and nature of behavioral responses affect the course of an epidemic

Speaker: 
Rebecca Tyson
Date: 
Mon, Jun 22, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

During an epidemic, the interplay of disease and opinion dynamics can lead to outcomes that are different from those predicted based on disease dynamics alone. Opinions and the behaviors they elicit are complex, so modeling them requires a measure of abstraction and simplification. In this talk, we develop a differential equation model that couples SIR-type disease dynamics with opinion dynamics. We assume a spectrum of opinions that change based on current levels of infection as well as interactions that to some extent amplify the opinions of like-minded individuals. Susceptibility to infection is based on the level of prophylaxis (disease avoidance) that an opinion engenders. In this setting, we observe how the severity of an epidemic is influenced by the distribution of opinions at disease introduction, the relative rates of opinion and disease dynamics, and the amount of opinion amplification. Some insight is gained by considering how the effective reproduction number is influenced by the combination of opinion and disease dynamics.

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Modeling intervention strategies for containing Covid-19 in Nursing homes with digital contact tracing

Speaker: 
Ilyssa Summer
Date: 
Mon, Jun 22, 2020
Location: 
Zoom
Abstract: 

Contact tracing is a key initiative in public health to contain Covid-19. At CarePredict, Inc., we developed a real-time digital contact tracing system that Long Term Care (LTC) facilities can use to rapidly identify and contain exposed, asymptomatic and symptomatic COVID-19 contacts. An SEIR deterministic model was developed to compare traditional and digital intervention methods for contact tracing in LTC Facilities. Data from our LTC facilities, skilled nursing homes, and nursing home data of residents affected by Covid-19, is utilized to form our parameter estimates and to inform the projections of the impact of contact tracing interventions. The model quantifies infection spread comparing across symptom tracing, manual contact tracing, PCR testing, and digital contact tracing in a nursing home setting. We computed the reproductive number per intervention type and compare parameter sensitivity to the base model to understand key components that can reduce spread.

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Not all interventions are equal for the height of the second peak

Speaker: 
Joost Jorritsma
Date: 
Mon, Jun 22, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

We present a simulation study of the spread of an epidemic like COVID-19 with temporary immunity on finite spatial and non-spatial network models. In particular, we assume that an epidemic spreads stochastically on a scale-free network and that each infected individual in the network gains a temporary immunity after its infectious period is over. After the temporary immunity period is over, the individual becomes susceptible to the virus again. When the underlying contact network is embedded in Euclidean geometry, we model three different intervention strategies that aim to control the spread of the epidemic: social distancing, restrictions on travel, and restrictions on maximal number of social contacts per node. Our first finding is that on a finite network, a long enough average immunity period leads to extinction of the pandemic after the first peak, analogous to the concept of ``herd immunity''. For each model, there is a critical average immunity duration $L_c$ above which this happens. Our second finding is that all three interventions manage to flatten the first peak (the travel restrictions most efficiently), as well as decrease the critical immunity duration $L_c$, but elongate the epidemic. However, when the average immunity duration $L$ is shorter than $L_c$, the price for the flattened first peak is often a high second peak: for limiting the maximal number of contacts, the second peak can be as high as 1/3 of the first peak, and twice as high as it would be without intervention. Thirdly, interventions introduce oscillations into the system and the time to reach equilibrium is, for almost all scenarios, much longer. We conclude that network-based epidemic models can show a variety of behaviors that are not captured by the continuous compartmental models.

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A simple criterion to design optimal nonpharmaceutical interventions for epidemic outbreaks

Speaker: 
Marco Tulio Angulo
Date: 
Mon, Jun 22, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

To mitigate the COVID-19 pandemic, much emphasis exists on implementing non-pharmaceutical interventions to keep the reproduction number below one. But using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significative economic and societal costs. Here we derive a simple and mathematically rigorous criterion for designing optimal transitory non- pharmaceutical interventions. We find that reducing the reproduction number below one is sufficient but not necessary. Instead, our criterion prescribes the required reduction in the reproduction number according to the maximum health services' capacity. To explore the implications of our theoretical results, we study the non- pharmaceutical interventions implemented in 16 cities during the COVID-19 pandemic. In particular, we estimate the minimal reduction of the contact rate in each city that is necessary to control the epidemic optimally. We also compare the optimal start of the intervention with the start of the actual interventions applied in each city. Our results contribute to establishing a rigorous methodology to guide the design of non-pharmaceutical intervention policies. Preprint: https://www.medrxiv.org/content/10.1101/2020.05.19.20107268v1

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