Analogies between SARS-CoV-2 infection dynamics and batch chemical reactor behavior

Two Chemical Engineers Look at the COVID-19 Pandemic

Chemical engineering involves a skill set that is transferrable to a broad range of other areas. A case in point is the work that is being done by chemical engineers to better understand and fight the COVID-19 epidemic. In this study, we consider a problem that has eluded the COVID-19 research community, which is nevertheless very tractable with a chemical engineering mindset: the true or intrinsic mortality rate of COVID-19, i.e., the fraction or percentage of COVID-19 infected people that die of the disease. We solve this problem in two locations (Spain and the state of New York) for the epidemic's first wave with a combination of daily death data, a fit of a computer simulation of an epidemiological model with adjustable parameters, and independent results of immunological blood testing on a random sample of the population. Parallels are drawn with the problem of determining the turnover frequency of a catalyst based on a similar combination of data and approaches. It is concluded from the study that the intrinsic mortality rate of COVID-19 was 1.45 ± 0.45 % during the first wave, a number that reflects OECD countries. By incorporating data on the age dependence of the mortality rate, a relationship f mort = (3.0 ± 0.7)×10-5 exp(0.1a), where a is the age in years, is tentatively put forward for the mortality rate as a fraction. This article is protected by copyright. All rights reserved.

Infection Units: A Novel Approach for Modeling COVID-19 Spread

A novel mechanistic model of COVID-19 spread is presented. The pool of infected individuals is not homogeneously mixed but is viewed as a passage into which individuals enter upon the contagion, through which they pass (in the manner of “plug flow”) and exit at their recovery points within a fixed time. Our novel concept of infection unit is defined. The model separately considers various population pools: two of symptomatic and asymptomatic infected patients; three different pools of recovered individuals; of assisted hospitalized patients; of the quarantined; and of those who die from COVID-19. Transmission of this disease is described by an infection rate function, modulated by an encounter frequency function. This definition makes redundant the addition of a separate pool for the exposed, as done in several other models. Simulations are presented. The effects of social restrictions and of quarantine policies on pandemic spread are demonstrated. The model differs conceptually from others of the kind in the description of the transmission dynamics of the disease. A set of experimental data is used to calibrate our model, which predicts the dynamic behavior of each of the defined pools during pandemic spread.

Modeling and Control of COVID-19 Transmission from a Perspective of Polymerization Reaction Dynamics

Due to the serious economic losses and deaths caused by COVID-19, the modeling and control of such a pandemic has become a hot research topic. This paper finds an analogy between a polymerization reaction and COVID-19 transmission dynamics, which will provide a novel perspective to optimal control measures. Susceptible individuals, exposed people, infected cases, recovered population, and the dead can be assumed to be specific molecules in the polymerization system. In this paper, a hypothetical polymerization reactor is constructed to describe the transmission of an epidemic, and its kinetic parameters are regressed by the least-squares method. The intensity of social distancing u is considered to the mixing degree of the reaction system, and contact tracing and isolation ρ can be regarded as an external circulation in the main reactor to reduce the concentration of active species. Through these analogies, this model can predict the peak infection, deaths, and end time of the epidemic under different control measures to support the decision-making process. Without any measures (u = 1.0 and ρ = 0), more than 90% of the population would be infected. It takes several years to complete herd immunity by nonpharmacological intervention when the proportion of deaths is limited to less than 5%. However, vaccination can reduce the time to tens to hundreds of days, which is related to the maximum number of vaccines per day.

Analysis on the spatio-temporal characteristics of COVID-19 in mainland China

COVID-19 has brought many unfavorable effects on humankind and taken away many lives. Only by understanding it more profoundly and comprehensively can it be soundly defeated. This paper is dedicated to studying the spatial-temporal characteristics of the epidemic development at the provincial-level in mainland China and the civic-level in Hubei Province. Moreover, a correlation analysis on the possible factors that cause the spatial differences in the epidemic's degree is conducted. After completing these works, three different methods are adopted to fit the daily-change tendencies of the number of confirmed cases in mainland China and Hubei Province. The three methods are the Logical Growth Model (LGM), Polynomial fitting, and Fully Connected Neural Network (FCNN). The analysis results on the spatial-temporal differences and their influencing factors show that: (1) The Chinese government has contained the domestic epidemic in early March 2020, indicating that the number of newly diagnosed cases has almost zero increase since then. (2) Throughout the entire mainland of China, effective manual intervention measures such as community isolation and urban isolation have significantly weakened the influence of the subconscious factors that may impact the spatial differences of the epidemic. (3) The classification results based on the number of confirmed cases also prove the effectiveness of the isolation measures adopted by the governments at all levels in China from another aspect. It is reflected in the small monthly grade changes (even no change) in the provinces of mainland China and the cities in Hubei Province during the study period. Based on the experimental results of curve-fitting and considering the time cost and goodness of fit comprehensively, the Polynomial(Degree = 18) model is recommended in this paper for fitting the daily-change tendency of the number of confirmed cases.

An epidemic model for non-first-order transmission kinetics

Compartmental models in epidemiology characterize the spread of an infectious disease by formulating ordinary differential equations to quantify the rate of disease progression through subpopulations defined by the Susceptible-Infectious-Removed (SIR) scheme. The classic rate law central to the SIR compartmental models assumes that the rate of transmission is first order regarding the infectious agent. The current study demonstrates that this assumption does not always hold and provides a theoretical rationale for a more general rate law, inspired by mixed-order chemical reaction kinetics, leading to a modified mathematical model for non-first-order kinetics. Using observed data from 127 countries during the initial phase of the COVID-19 pandemic, we demonstrated that the modified epidemic model is more realistic than the classic, first-order-kinetics based model. We discuss two coefficients associated with the modified epidemic model: transmission rate constant k and transmission reaction order n. While k finds utility in evaluating the effectiveness of control measures due to its responsiveness to external factors, n is more closely related to the intrinsic properties of the epidemic agent, including reproductive ability. The rate law for the modified compartmental SIR model is generally applicable to mixed-kinetics disease transmission with heterogeneous transmission mechanisms. By analyzing early-stage epidemic data, this modified epidemic model may be instrumental in providing timely insight into a new epidemic and developing control measures at the beginning of an outbreak.

COVID-19: Mechanistic model calibration subject to active and varying non-pharmaceutical interventions

Mathematical models are useful in epidemiology to understand COVID-19 contagion dynamics. We aim to demonstrate the effectiveness of parameter regression methods to calibrate an established epidemiological model describing infection rates subject to active, varying non-pharmaceutical interventions (NPIs). We assess the potential of established chemical engineering modelling principles and practice applied to epidemiological systems. We exploit the sophisticated parameter regression functionality of a commercial chemical engineering simulator with piecewise continuous integration, event and discontinuity management. We develop a strategy for calibrating and validating a model. Our results using historic data from 4 countries provide insights into on-going disease suppression measures, while visualisation of reported data provides up-to-date condition monitoring of the pandemic status. The effective reproduction number response to NPIs is non-linear with variable response rate, magnitude and direction. Our purpose is developing a methodology without presenting a fully optimised model, or attempting to predict future course of the COVID-19 pandemic.