A New Approach to the Dynamic Modeling of an Infectious Disease

Abstract

In this work we propose a delay differential equation as a lumped parameter or compartmental infectious disease model featuring high descriptive and predictive capability, extremely high adaptability and low computational requirement. Whereas the model has been developed in the context of COVID-19, it is general enough to be applicable mutatis mutandis to other diseases as well. Our fundamental modeling philosophy consists of a decoupling of public health intervention effects, immune response effects and intrinsic infection properties into separate terms. All parameters in the model are directly related to the disease and its management; we can measure or calculate their values a priori basis our knowledge of the phenomena involved, instead of having to extrapolate them from solution curves. Our model can accurately predict the effects of applying or withdrawing interventions, individually or in combination, and can quickly accommodate any newly released information regarding, for example, the infection properties and the immune response to an emerging infectious disease. After demonstrating that the baseline model can successfully explain the COVID-19 case trajectories observed all over the world, we systematically show how the model can be expanded to account for heterogeneous transmissibility, detailed contact tracing drives, mass testing endeavours and immune responses featuring different combinations of limited-time sterilizing immunity, severity-reducing immunity and antibody dependent enhancement.

Impact of reproduction number on the multiwave spreading dynamics of COVID-19 with temporary immunity: A mathematical model

“…In this variability however also lies our model’s primary strength. The model structure makes it easy to incorporate any kind of immune response ( Shayak and Sharma, 2020 ). The computational requirement is negligible, with the run for each Notional City taking about one second on a personal computer.…”

Impact of Immediate and Preferential Relaxation of Social and Travel Restrictions for Vaccinated People on the Spreading Dynamics of COVID-19 : a Model-Based Analysis

“…We use a compartmental or lumped parameter delay differential equation model developed by our group to analyse the various situations of interest. We have selected this model because all parameters here are directly related to the disease or to control measures 17 . This feature enables the model to generate realistic epidemiological curves with default assumptions 18,19 and make subtle predictions regarding the spreading trajectories with temporary immunity 20 .…”

COVID-19 Spreading Dynamics in an Age-Structured Population with Selective Relaxation of Restrictions for Vaccinated Individuals : a Mathematical Modeling Study

“…We use a compartmental or lumped parameter delay differential equation model developed by our group 21 . We have selected this model because all parameters here are directly related to the disease or to control measures, and because it can be easily extended to accommodate vaccination.…”

“…The per-case spreading rate, which we call m 0 , is the product of two quantities – the rate q 0 at which a random person (and hence an at large case who is unaware of infectious nature) interacts with other people, and the probability P 0 that an interaction with a susceptible target results in a transmission. q 0 is governed by the degree of social restrictions in place while P 0 is determined by masking and sanitization; collectively, m 0 embodies the effects of non-pharmaceutical interventions [21]. q 0 happens to be available as a parameter from Literature; this fact will play an important role later.…”

“…Equation (2)uses delays rather than inverse-rates to express infection durations, which enables it to make very realistic predictions. For further details of derivation, we must refer to our prior study [21].…”