A hybrid discrete-continuum model of immune responses to SARS-CoV-2 infection in the lung alveolar region, with a focus on interferon induced innate response.

We develop a lattice-based, hybrid discrete-continuum modeling framework for SARS-CoV-2 exposure and infection in the human lung alveolar region, or parenchyma, the massive surface area for gas exchange. COVID-19 pneumonia is alveolar infection by the SARS-CoV-2 virus significant enough to compromise gas exchange. The modeling framework orchestrates the onset and progression of alveolar infection, spatially and temporally, beginning with a pre-immunity baseline, upon which we superimpose multiple mechanisms of immune protection conveyed by interferons and antibodies. The modeling framework is tunable to individual profiles, focusing here on degrees of innate immunity, and to the evolving infection-replication properties of SARS-CoV-2 variant strains. The model employs partial differential equations for virion, interferon, and antibody concentrations governed by diffusion in the thin fluid coating of alveolar cells, species and lattice interactions corresponding to sources and sinks for each species, and multiple immune protections signaled by interferons. The spatial domain is a two-dimensional, rectangular lattice of alveolar type I (non-infectable) and type II (infectable) cells with a stochastic, species-concentration-governed, switching dynamics of type II lattice sites from healthy to infected. Once infected, type II cells evolve through three phases: an eclipse phase during which RNA copies (virions) are assembled; a shedding phase during which virions and interferons are released; and then cell death. Model simulations yield the dynamic spread of, and immune protection against, alveolar infection and viral load from initial sites of exposure. We focus in this paper on model illustrations of the diversity of outcomes possible from alveolar infection, first absent of immune protection, and then with varying degrees of four known mechanisms of interferon-induced innate immune protection. We defer model illustrations of antibody protection to future studies. Results presented reinforce previous recognition that interferons produced solely by infected cells are insufficient to maintain a high efficacy level of immune protection, compelling additional mechanisms to clear alveolar infection, such as interferon production by immune cells and adaptive immunity (e.g., T cells). This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Estimates of the collective immunity to COVID-19 derived from a stochastic cellular automaton based framework.

In the context of the propagation of infectious diseases, when a sufficient degree of immunisation is achieved within a population, the spread of the disease is ended or significantly decreased, leading to collective immunity, meaning the indirect protection given by immune individuals to susceptible individuals. Here we describe the estimates of the collective immunity to COVID-19 from a stochastic cellular automaton based model designed to emulate the spread of SARS-CoV-2 in a population of static individuals interacting only via a Moore neighbourhood of radius one, with a view to analyze the impact of initially immune individuals on the dynamics of COVID-19. This impact was measured by comparing a progression of initial immunity ratio-the percentage of immunised individuals before patient zero starts infecting its neighbourhood-from 0 to 95% of the initial population, with the number of susceptible individuals not contaminated, the peak value of active cases, the total number of deaths and the emulated pandemic duration in days. The influence of this range of immunities over the model was tested with different parameterisations regarding the uncertainties involved in the model such as the durations of the cellular automaton states, the contamination contributions of each state and the state transition probabilities. A collective immunity threshold of 55 % ± 2.5 % on average was obtained from this procedure, under four distinct parameterisations, which is in tune with the estimates of the currently available medical literature, even increasing the uncertainty of the input parameters.

Using Cellular Automata to Compare SARS-CoV-2 Infectiousness in Different POIs and Under Different Conditions

In this paper, we propose a stochastic model based on cellular automata and graphs to explore the spread of infectious viruses (like SARS-CoV-2) in closed rooms. We also present a simulator implementing this model which allows studying how different policies affect the spread of viruses. As we show, the simulator can be used to explore scenarios in various points of interest (POIs) like shops, public trams or fitness centres. It could be useful for policymakers to check (by changing the parameters of the simulations) the effectiveness of different regulations like limiting the maximum occupancy of POIs and mandating the usage of face masks to decrease the spread of aerosols. The simulator can also be used to compare the hazard level that different kinds of POIs pose. Also, the simulations can be visualised and showed to the public to increase support for the introduced measures and obedience to restrictions. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Intelligent agent model for simulating pedestrian traffic at urban trade fairs during the COVID-19 pandemic

The COVID-19 pandemic highlighted the need for new approaches to the urban environment. Among them, physical distancing is intended to minimize contagion and safeguard general welfare. In the present research, a simulated model was designed to identify close contacts during pedestrian traffic in specific urban activities such as a trade fair. This research type was applied and of quasi-experimental design, a parametric simulation model based on intelligent agents was developed at the micro level in urban trade fair scenarios. initially, theoretical trade fair configurations were compared, considering the shape of the walkable space and the arrangement of trade stands. Then, a manipulation of particular parameters is performed, among them, the probability of making a stall visible and the probability of stopping in case of direct contact or collision. Finally, the results were compared using statistical correlations, the PerMANOVA test, Games-Howell and the graphical analysis of the micro-simulated pedestrian behaviors by the developed model. It is concluded that the model is valid for theoretical pedestrian traffic models for the five simulated urban fairground scenarios.

Assessing the Impact of Contact Tracing, Quarantine and Red Zone on the Dynamical Evolution of the Covid-19 Pandemic using the Cellular Automata Approach and the Resulting Mean Field System: A Case study in Mauritius.

A cellular automaton (CA) depicting the dynamics of the Covid-19 pandemic, is set up. Unlike the classic CA models, the present CA is an enhanced version, embodied with contact tracing, quarantine and red zones to model the spread of the Covid-19 pandemic. The incubation and illness periods are assimilated in the CA system. An algorithm is provided to showcase the rules governing the CA, with and without the enactment of red zones. By means of mean field approximation, a nonlinear system of delay differential equations (DDE) illustrating the dynamics of the CA is emanated. The concept of red zones is incorporated in the resulting DDE system, forming a DDE model with red zone. The stability analysis of both systems are performed and their respective reproduction numbers are derived. The effect of contact tracing and vaccination on both reproduction numbers is also investigated. Numerical simulations of both systems are conducted and real time Covid-19 data in Mauritius for the period ranged from 5 March 2021 to 2 September 2021, is employed to validate the model. Our findings reveal that a combination of both contact tracing and vaccination is indispensable to attenuate the reproductive ratio to less than 1. Effective contact tracing, quarantine and red zones have been the key strategies to contain the Covid-19 virus in Mauritius. The present study furnishes valuable perspectives to assist the health authorities in addressing the unprecedented rise of Covid-19 cases.

The influence of immune individuals in disease spread evaluated by cellular automaton and genetic algorithm.

BACKGROUND AND OBJECTIVE: One of the main goals of epidemiological studies is to build models capable of forecasting the prevalence of a contagious disease, in order to propose public health policies for combating its propagation. Here, the aim is to evaluate the influence of immune individuals in the processes of contagion and recovery from varicella. This influence is usually neglected. METHODS: An epidemic model based on probabilistic cellular automaton is introduced. By using a genetic algorithm, the values of three parameters of this model are determined from data of prevalence of varicella in Belgium and Italy, in a pre-vaccination period. RESULTS: This methodology can predict the varicella prevalence (with average relative error of 2%-4%) in these two European countries. Belgium data can be explained by ignoring the role of immune individuals in the infection propagation; however, Italy data can be explained by considering contagion exclusively mediated by immune individuals. CONCLUSIONS: The role of immune individuals should be accurately delineated in investigations on the dynamics of disease propagation. In addition, the proposed methodology can be adapted for evaluating, for instance, the role of asymptomatic carriers in the novel coronavirus spread.

A Review of Multi-Compartment Infectious Disease Models.

Multi-compartment models have been playing a central role in modelling infectious disease dynamics since the early 20th century. They are a class of mathematical models widely used for describing the mechanism of an evolving epidemic. Integrated with certain sampling schemes, such mechanistic models can be applied to analyse public health surveillance data, such as assessing the effectiveness of preventive measures (e.g. social distancing and quarantine) and forecasting disease spread patterns. This review begins with a nationwide macromechanistic model and related statistical analyses, including model specification, estimation, inference and prediction. Then, it presents a community-level micromodel that enables high-resolution analyses of regional surveillance data to provide current and future risk information useful for local government and residents to make decisions on reopenings of local business and personal travels. r software and scripts are provided whenever appropriate to illustrate the numerical detail of algorithms and calculations. The coronavirus disease 2019 pandemic surveillance data from the state of Michigan are used for the illustration throughout this paper.