Matching Theory and Evidence on Covid-19 using a Stochastic Network SIR Model

This paper develops an individual-based stochastic network SIR model for the empirical analysis of the Covid-19 pandemic. It derives moment conditions for the number of infected and active cases for single as well as multigroup epidemic models. These moment conditions are used to investigate identification and estimation of recovery and transmission rates. The paper then proposes simple moment-based rolling estimates and shows them to be fairly robust to the well-known under-reporting of infected cases. Empirical evidence on six European countries match the simulated outcomes, once the under-reporting of infected cases is addressed. It is estimated that the number of reported cases could be between 3 to 9 times lower than the actual numbers. Counterfactual analysis using calibrated models for Germany and UK show that early intervention in managing the infection is critical in bringing down the reproduction numbers below unity in a timely manner

Adaptive Social Distancing Strategies for Controlling Infection Inequality in Emerging Infectious Diseases

People fare in outbreaks of emerging infections based on social factors shaping their exposure and vulnerability to the virus. This different exposure cause a disproportionate share of prevalence among people with various socioeconomic statuses. Therefore, socioeconomic-based control strategies are needed to control the discrepancy in prevalence among socioeconomic groups. We propose and analyze a SIR mathematical model that is grouped based on individuals\u27 income level (representing socioeconomic status). For the model\u27s parameter, we use properties of a real-world social network of individuals residing in New Orleans, Louisiana. We then distribute the social distancing practice among different groups to minimize a multi-objective function of infection characteristics (final epidemic size) and the discrepancy of prevalence among them (infection inequality). Our result confirms the importance of the heterogeneous distribution of social distancing practices among various socioeconomic groups to reduce observed infection inequality. At the same time, it does not considerably impact the final epidemic size

Agent-based modeling and System Dynamics modeling on transmission of Tuberculosis in Saskatchewan

The desire to better understand the transmission of infectious disease in the real world has motivated the representation of epidemic diffusion processes in the context of qualitative simulation as a computational model on provincial and community levels. In this thesis, we have developed both agent-based models and System Dynamics models within the context of M. Tuberculosis (TB) transmission in Saskatchewan and a community in Saskatchewan to evaluate the efficiency of prevention programs such as contact tracing investigation. New insights about how dynamic models and agent-based models can assist policy development and decision making in disease control will be generated. Moreover, we sought to compare these two modeling approaches to gain insights in TB diffusion in Saskatchewan as well as guidance in choosing the appropriate modeling approach for particular problems

Agent-Based Markov Modeling for Improved COVID-19 Mitigation Policies

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Agent-Based Markov Modeling for Improved COVID-19 Mitigation Policies

The year 2020 saw the covid-19 virus lead to one of the worst global pandemics in history. As a result, governments around the world have been faced with the challenge of protecting public health while keeping the economy running to the greatest extent possible. Epidemiological models provide insight into the spread of these types of diseases and predict the e_ects of possible intervention policies. However, to date, even the most data-driven intervention policies rely on heuristics. In this paper, we study how reinforcement learning (RL) and Bayesian inference can be used to optimize mitigation policies that minimize economic impact without overwhelming hospital capacity. Our main contributions are (1) a novel agent-based pandemic simulator which, unlike traditional models, is able to model _ne-grained interactions among people at speci_c locations in a community; (2) an RL- based methodology for optimizing _ne-grained mitigation policies within this simulator; and (3) a Hidden Markov Model for predicting infected individuals based on partial observations regarding test results, presence of symptoms, and past physical contacts

Global Dynamics for a Novel Differential Infectivity Epidemic Model with Stage Structure

A novel differential infectivity epidemic model with stage structure is formulated and studied. Under biological motivation, the stability of equilibria is investigated by the global Lyapunov functions. Some novel techniques are applied to the global dynamics analysis for the differential infectivity epidemic model. Uniform persistence and the sharp threshold dynamics are established; that is, the reproduction number determines the global dynamics of the system. Finally, numerical simulations are given to illustrate the main theoretical results

The mathematical modelling of the transmission dynamics of HIV/AIDS and the impact of antiviral therapies

Thesis presented for the degree of Doctor of Philosophy, Department of Electronics and Mathematics, Faculty of Science, Technology and Design, the University of LutonThis thesis is concerned with the structure, analysis and numerical solution of the mathematical models used to estimate the transmission dynamics of the Human Immunodeficiency Virus (HIV)) the causative agent of Acquired Immune Deficiency Syndrome (AIDS). Investigations show that the devised deterministic mathematical models in term of system of first-order non-linear ordinary differential equations (ODEs) follow the stochastic nature of the problem at any time. In this thesis a generic form of the deterministic mathematical models is introduced which mirrors the transmission dynamics of HIV/AIDS in populations with different states of affairs, which leads to the division of large-scale and complex mathematical models. When analysing and;or solving a large-scale system of ODEs numerically, the key element in speeding up the process is selecting the maximum possible time step. This work introduces some new techniques used to estimate the maximum possible time step, avoiding the appearance of chaos and divergence in the solution when they are not features of the system. The solution to these mathematical models are presented graphically and numerically, aiming to identify the effect of the anti-HIV therapies and sex education in controlling the disease. The numerical results presented in this thesis indicate that lowering the average number of sexual partners per year is more effective in controlling the disease than the current anti-HIV treatments. For the purpose of this study the mathematical software 'Mathematica 3.0' was used to solve the system of differential equations, modelling HIV/AIDS propagation. This package also provided the graphical detail incorporated in the thesis