Mathematical modelling of infectious diseases

Summary

Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc. History The modelling of infectious diseases is a tool that has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. The first scientist who systematically tried to quantify causes of death was John Graunt in his book Natural and Political Observations made upon the Bills of Mortality, in 1662. The bills he studied were listings of

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Modeling infectious disease dynamics towards informed public health interventions, with applications on COVID-19 and cholera

Joseph Chadi Benoit Lemaitre

Emerging and existing infectious diseases pose a constant threat to individuals and communities across the world. In many cases, the burden of these diseases is preventable through public health interventions. However, taking the right decisions and designing effective policies is an intricate task: epidemics are complex phenomena resulting from the interaction between the environment, pathogens, individuals, and societies. Modeling offers a principled way to reason about infectious disease dynamics from scarce and biased information and to guide decision-makers towards effective policies. This thesis tackles selected topics in cholera and COVID-19 modeling towards informed public-health decisions. These two contrasting diseases were associated by a twist of fate, but also through the lens of a common modeling approach: compartmental, SIR-based, models are conditioned on the available evidence using computer-age statistical inference frameworks. A set of five models is developed, each tackling a different facet of the spread and control of these two infectious diseases. Each model aims at answering questions related to either the understanding of the mechanisms behind disease transmission, the projection of the future dynamics under different scenarios, or the assessment of the effectiveness of past interventions. Moreover, a novel application of epidemiological models to the formal design of control policies is proposed. Optimal control provides a rigorous framework to identify the most effective control measures under a set of operational constraints, providing a benchmark on what it is possible to achieve with the available resources.The results presented in this thesis range from scientific insight on the relationship between cholera and rainfall in Juba, South Sudan to the COVID Scenario Pipeline which produces reports used to inform the response to the COVID-19 pandemic of different governmental entities. Furthermore, the effectiveness of the non-pharmaceutical interventions against COVID-19 in Switzerland is evaluated; and so is the probability of eliminating cholera from Haiti under different scenarios of mass vaccination campaigns. Finally, the development of an optimal control framework towards the effective spatial allocation of vaccines against SARS-CoV-2 in Italy closes this conversation of models.The present thesis demonstrates how infectious disease modeling enables informed decision-making by projecting the uncertainties under the light of the available evidence. It also highlights the effort needed to tailor the models and inference methods to the specificities of the transmission setting and the research question considered. From insights on transmission pathways to weekly reports aimed at decision-makers, it explores different applications of infectious disease modeling. Methods developed along the way enrich the toolbox available to modelers, to guide policy decisions further towards a reduction of the burden of infectious diseases on communities.

EPFL2021

Epidemic monitoring systems engaged in accurate discovery of infected individuals enable better understanding of the dynamics of epidemics and thus may promote effective disease mitigation or prevention. Currently, infection discovery systems require either physical participation of potential patients or provision of information from hospitals and health-care services. While social media has emerged as an increasingly important knowledge source that reflects multiple real world events, there is only a small literature examining how social media information can be incorporated into computational epidemic models. In this paper, we demonstrate how social media information can be incorporated into and improve upon traditional techniques used to model the dynamics of infectious diseases. Using flu infection histories and social network data collected from 264 students in a college community, we identify social network signals that can aid identification of infected individuals. Extending the traditional SIRS model, we introduce and illustrate the efficacy of an Online-Interaction-Aware Susceptible-Infected-Recovered-Susceptible (OIA-SIRS) model based on four social network signals for modeling infection dynamics. Empirical evaluations of our case study, flu infection within a college community, reveal that the OIA-SIRS model is more accurate than the traditional model, and also closely tracks the real-world infection rates as reported by CDC ILINet and Google Flu Trend

ACM2015

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Multi-port DC-DC converters are an attractive solution for highly flexible and efficient interface of different elements of DC grids (e.g., sources, loads, energy storage). This paper provides an analytic solution for the natural power sharing characteristics of a galvanically isolated three-port resonant DC-DC converter. A DC-transformer operation mode is considered, with two ports actively transferring power to a third port. The mathematical model reveals that the power sharing characteristics are tightly dominated by the resonant tank parameters, even though they are also dependent on the differential voltage at the input terminals and the system losses. The accuracy of the proposed model is verified by an experimental validation on a lab-scale prototype.

IEEE2019

Modeling infectious disease dynamics towards informed public health interventions, with applications on COVID-19 and cholera

Joseph Chadi Benoit Lemaitre

EPFL2021