Compartmental Models of the COVID-19 Pandemic for Physicians and Physician-Scientists

Abou-Ismail, Anas. “Compartmental Models of the COVID-19 Pandemic for Physicians and Physician-Scientists.” SN Comprehensive Clinical Medicine, June 2020, pp. 1–7. PubMed, doi:10.1007/s42399-020-00330-z.

This article provides an overview of the derivation of the SIR, SEIR, and SUQC compartmental models. The first two models can be found in my other post, SEIR Modeling of the Italian Epidemic of SARS-CoV-2 Using Computational Swarm Intelligence. Here, I will discuss the derivation of the SUQC model and a few other terms.

The basic reproductive number (the number of people a contagious person infects) for an infectious disease is: $R_0=\frac{\beta}{\gamma}$, or the ratio between the rate at which people move from Susceptible to Infected over the rate at which people move from Infected to Removed (pg 856)

The herd immunity threshold (HIT) is “the minimum ratio of individuals that must become immune to a disease so that it would die out” (pg 857). It is given as: $HIT=1-\frac{1}{R_0}$.

The SUQC model was used by Zhao et al. to describe the progression between Susceptible, Un-quarantined Infected, Quarantined Infected, and Confirmed Infected (pg 858). The model is defined as follows (where N is the total population):

$I(t)=U(t)+Q(t)+C(t)$

$\frac{dS}{dt}=\frac{-\alpha*U(t)*S(t)}{N}$

$\frac{dU}{dt}=\frac{\alpha*U(t)*S(t)}{N}-\gamma_1*U(t)$

$\frac{dQ}{dt}=\gamma_1*U(t)-\beta*Q(t)$

$\frac{dC}{dt}=\beta*Q(t)$

Zhao S, Chen H, et al. Modeling the epidemic dynamics and control of COVID-19 outbreak in China. Quant Biol. 2020;8:11–9. https:// doi.org/10.1007/s40484-020-0199-0.