Open AccessA model for the spread of infectious diseases compatible with case data
Author(s) -
Norden E. Huang,
Fangli Qiao,
Qian Wang,
Hong Qian,
KaKit Tung
Publication year - 2021
Publication title -
proceedings - royal society. mathematical, physical and engineering sciences
Language(s) - English
Resource type - Journals
eISSN - 1471-2946
pISSN - 1364-5021
DOI - 10.1098/rspa.2021.0551
Subject(s) - herd immunity , epidemic model , epidemiology , population , basic reproduction number , covid-19 , infectious disease (medical specialty) , econometrics , disease , virology , demography , statistics , medicine , mathematics , environmental health , sociology , pathology
For epidemics such as COVID-19, with a significant population having asymptomatic, untested infection, model predictions are often not compatible with data reported only for the cases confirmed by laboratory tests. Additionally, most compartmental models have instantaneous recovery from infection, contrary to observation. Tuning such models with observed data to obtain the unknown infection rate is an ill-posed problem. Here, we derive from the first principle an epidemiological model with delay between the newly infected (N ) and recovered (R ) populations. To overcome the challenge of incompatibility between model and case data, we solve for the ratios of the observed quantities and show that log(N (t )/R (t )) should follow a straight line. This simple prediction tool is accurate in hindcasts verified using data for China and Italy. In traditional epidemiology, an epidemic wanes when much of the population is infected so that ‘herd immunity’ is achieved. For a highly contagious and deadly disease, herd immunity is not a feasible goal without human intervention or vaccines. Even before the availability of vaccines, the epidemic was suppressed with social measures in China and South Korea with much less than 5% of the population infected. Effects of social behaviour should be and are incorporated in our model.