PMC:7029158 / 5950-8718 JSONTXT

{"target":"http://pubannotation.org/docs/sourcedb/PMC/sourceid/7029158","sourcedb":"PMC","sourceid":"7029158","source_url":"https://www.ncbi.nlm.nih.gov/pmc/7029158","text":"Time-dependent dynamic model\nOn January 23rd, 2020, Wuhan, the epicenter of the current coronavirus outbreak, announced the implementation of travel restriction as strategy for controlling the infection. Following this announcement, many other cities and provinces of China decided to enforce similar measures. In the meantime, many other control measures have been adopted, like convincing all the residents to stay at home and avoid contacts as much as possible. From the mathematical point of view, this can significantly contribute to decreasing the contact rate c among the persons. On the other hand, also from January 23rd, 2020, gradually increasing numbers of 2019-nCoV testing kits were sent to Wuhan from other provinces, gradually shortening the time period of diagnosis (i.e. the value of δI increases greatly). Considering these control strategies, we adapted our previous model (Tang et al., 2020) as time-dependent dynamic system, by taking January 23rd, 2020 as the newly initial time:S’=−(βc(t)+c(t)q(1−β))S(I+θA)+λSq,E’=βc(t)(1−q)S(I+θA)−σE,I’=σϱE−(δI(t)+α+γI)I,A’=σ(1−ϱ)E−γAA,Sq’=(1−β)c(t)qS(I+θA)−λSq,Eq’=βc(t)qS(I+θA)−δqEq,H’=δI(t)I+δqEq−(α+γH)H,R’=γII+γAA+γHH,\nHere, we assume that the contact rate c(t) is a decreasing function with respect to time t, which is given byc(t)=(c0−cb)e−r1t+cb,where c0 is the contact rate at the initial time (i.e. January 23rd, 2020), cb is the minimum contact rate under the current control strategies, and r1 is the exponential decreasing rate of the contact rate. Definitely, there are c(0)=c0 and limt→∞c(t)=cb with cb\u003cc0. This is basically to assume the contacts are decreasing and the change rate per contact is r1. This constant provides a measure of public health intervention improvement in terms of self-isolation of all including susceptible individuals in the period.\nSimilarly, we set δI(t) to be an increasing function with respect to time t, equivalently, the period of diagnosis 1/δI(t) is a decreasing function of t with the following form:1δI(t)=(1δI0−1δIf)e−r2t+1δIf.here, δI0 is the diagnose rate at the initial time with δI(0)=δI0, δIf is the fastest diagnose rate with limt→∞δI(0)=δIf, and r2 is the exponential decreasing rate. This rate is highly relevant to the resources available in the epicenter.\nUsing the formula we derived in (Tang et al., 2020) but replacing the constant contact rate c and δI with the aforementioned time-dependent coefficients to reflect the evolving public health interventions and resources available, we definedRd(t)=[βϱc(t)(1−q)δI(t)+α+γI+βc(t)θ(1−ϱ)(1−q)γA]S0.as the effective daily reproduction ratio, to measure the ‘daily reproduction number’, the number of new infections induced by a single infected individual during his/her infectious period per 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