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 with such changes as necessary 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 temporary sterilizing immunity, severity-reducing immunity and antibody dependent enhancement.
Highlights
We split this discussion into two Sections, one general and the second more specific.1.1
Overview of disease modeling approaches With the spread of COVID-19 like wildfire all over the world, infectious disease dynamics has suddenly been promoted from a niche area of dynamical systems theory to the foremost topic in applied mathematics and sciences research
This concludes our summary of the different approaches in existence to the mathematical modeling of infectious diseases in general and COVID-19 in particular
Summary
We split this discussion into two Sections, one general and the second more specific. A lattice site contracts the infection with a certain user-defined probability if its one or more neighbours are infectious, and progresses through the successive states with user-defined probabilities and durations The advantage of this model is that it is the closest representation of reality and is capable of extreme accuracy. – Data-driven model: These models take the existing data of COVID-19 spread over the past week or month (or longer) and use machine learning etc methods to generate a forecast for the week or month They pay little or no attention to the underlying processes driving the spread of the disease. This concludes our summary of the different approaches in existence to the mathematical modeling of infectious diseases in general and COVID-19 in particular. What we propose in this article is a lumped parameter model; we shall present a summary of the state of the art in this area
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