A mathematical study of basic reproduction R0 and its significance in
controlling of corona-virus (COVID-19) disease transmission
Abstract
The basic reproduction number of an infectious agent is the average
number of infections one case can generate over the course of the
infectious period, in a naive, uninfected population. This primer
article focuses on the basic reproduction number, R0, for infectious
diseases, and other reproduction numbers related to $R_0$ that are
useful in guiding control strategies. Beginning with a simple population
model, the concept is developed for a threshold value of R0 determining
whether or not the disease dies out. The next generation matrix method
of calculating R0 in a compartmental model is described and illustrated.
To address control strategies reproduction numbers are defined and these
theoretical ideas are then applied to models that are formulated for
different SI, SI with incubation delay, SIR, SEIR and SEQIR the novel
coronavirus (2019-nCoV) infection model , the reproduction number has
been found to vary, reflecting the dynamics of transmission of the
coronavirus outbreak as well as the case reporting rate. If $R_0
> 1,$ then the number of latently infected individuals
exponentially grows. However, if $R_0 < 1$ (e.g. due to
quarantine measures and contact restrictions imposed by public
authorities), then the number of infected decays exponentially. We then
consider the available data on the disease development in different
countries to show that there are three possible patterns: growth
dynamics, growth- decays dynamics, and patchy dynamics. During this
period of time, the growth rate of the total number of infected was
gradually decreasing.