Mathematics

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
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
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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Impacts on community transmission and disease burden of a clinical prediction tool to prioritize limited COVID testing

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

Community spread of coronavirus disease 2019 (COVID-19) continues to be high in many areas, likely due, in part, to insufficient testing and contact tracing. As regional test kit shortages are likely to continue with increased transmission, it is important that available testing capacity be used effectively. To date, testing for COVID-19 has largely been restricted to persons reporting symptoms, with no additional criteria being systematically employed to select who is tested. In situations when testing capacity is limited, we propose the use of a clinical prediction rule to allow for prioritized testing of people who are most likely to test positive for COVID-19. Using data from the University of Utah Health system, we developed a robust, deployable clinical prediction rule which incorporates data on demographics and clinical characteristics to predict which patients are most likely to test positive. We then incorporated prioritized testing into a stochastic SEIR model for COVID-19 to measure changes in disease burden compared to a model with indiscriminate testing. Our best performing clinical prediction rule achieved an AUC of 0.7. When incorporated into the SEIR model, prioritized testing resulted in a delay in the timing of the infection peak, a meaningful reduction in both the total number of infected individuals and the peak height of the infection curve, and thus a reduction in the excess demand on local hospital resources. These effects were strongest for lower values of Rt and higher proportions of infected individuals seeking testing.

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Spatiotemporal Transmission Dynamics of COVID-19 in Spain

Speaker: 
Ashok Krishnamurthy
Date: 
Mon, Jun 22, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
Abstract: 

Mathematical modelling of infectious diseases is an interdisciplinary area of increasing interest. Tracking and forecasting the full spatio-temporal evolution of an epidemic can help public health officials to plan their emergency response and health care. We present advanced methods of spatial data assimilation to epidemiology, in this case to the ebb and flow of COVID-19 across the landscape of Spain. Data assimilation is a general Bayesian technique for repeatedly and optimally updating an estimate of the current state of a dynamic model. We present a stochastic spatial Susceptible-Exposed-Infectious-Recovered-Dead (S-E-I-R-D) compartmental model to capture the transmission dynamics and the spatial spread of the ongoing COVID-19 outbreak in Spain. In this application the machinery of data assimilation acts to integrate incoming daily incidence data into a fully spatial population model, within a Bayesian framework for the tracking process. For the current outbreak in Spain we use registered data (CCAA-wide daily counts of total COVID-19 cases, recovered, hospitalized, and confirmed dead) from the Instituto de Salud Carlos III (ISCIII) situation reports. Our simulations show good correspondences between the stochastic model and the available sparse empirical data. A comparison between daily incidence data set and our SEIRD model coupled with Bayesian data assimilation highlights the role of a realization conditioned on all prior data and newly arrived data. In general, the SEIRD model with data assimilation gives a better fit than the model without data assimilation for the same time period. Our analyses may shed light more broadly on how the disease spreads in a large geographical area with places where no empirical data is recorded or observed. The analysis presented herein can be applied to a large class of compartmental epidemic models. It is important to remember that the model type is not particularly crucial for data assimilation, the Bayesian framework is the key. Data assimilation neither requires nor presupposes that the model of the infectious disease be in the family of S-I-R compartmental models. The projected number of newly infected and death cases up to August 1, 2020 are estimated and presented.

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Fast spread of SARS-CoV-2 in China, Europe and the US

Speaker: 
Ruian Ke
Date: 
Mon, Jun 22, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
Abstract: 

SARS-CoV-2 is a novel pathogen causes the COVID-19 pandemic. Some of the basic epidemiological parameters, such as the exponential epidemic growth rate and R0 are debated. We collected and analyzed data from China, eight European countries and the US using a variety of inference approaches. In all countries, the early epidemic grew exponentially at rates between 0.19-0.29/day (epidemic doubling times between 2.4-3.7 days). I will discuss the appropriate serial intervals to estimate the basic reproductive number R0 and argue that existing evidence suggests a highly infectious virus with an R0 likely between 4.0 and 7.1. Further, we found that similar levels of intervention efforts are needed, no matter the goal is mitigation or containment. Early, strong and comprehensive intervention efforts to achieve greater than 74-86% reduction in transmission are necessary.

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Characterizing the spread of COVID-19 in Canada and the USA

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

Provincial and US state case, hospitalization, and death data can be characterized by relatively long periods of nearly constant growth/decline along with some large outbreaks. This talk will compare the spread in the different jurisdictions and how it has changed with relaxed social distancing measures.

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