A time delay dynamic system with external source for the local outbreak of 2019-nCoV

Abstract

How to model the 2019 CoronaVirus (2019-nCov) spread in China is one of the most urgent and interesting problems in applied mathematics. In this paper, we propose a novel time delay dynamic system with external source to describe the trend of local outbreak for the 2019-nCoV. The external source is introduced in the newly proposed dynamic system, which can be considered as the suspected people travel to different areas. The numerical simulations exhibit the dynamic system with the external source is more reliable than the one without it, and the rate of isolation is extremely important for controlling the increase of cumulative confirmed people of 2019-nCoV. Based on our numerical simulation results with the public data, we suggest that the local government should have some more strict measures to maintain the rate of isolation. Otherwise the local cumulative confirmed people of 2019-nCoV might be out of control.

Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China

“…The fact that the observed growth behavior appears for all provinces during the transient phase between onset and saturation suggests that this aspect of the dynamics is determined by fundamental principles that are at work and robust with respect to variation of other parameters that typically shape the temporal evolution of epidemic processes. Three questions immediately arise, (i) what may be the reason for this functional dependency, (ii) are provinces other than Hubei mostly driven by export cases from Hubei and therefore follow a similar functional form in case counts as suggested by preliminary studies discussing the influence of human travel (14)(15)(16), or, alternatively, (iii) is the scaling law a consequence of endogenous and basic epidemiological processes, caused by a balance between transmission events and containment efforts.…”

Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 outbreak in Mainland China

“…The universality of the scaling relation t µ with similar exponents µ is evidence that this aspect of the dynamics is determined by fundamental principles that are at work and robust with respect to variation of other parameters that typically shape the temporal evolution of epidemic processes. Three questions immediately arise, (i) what may be the reason for this functional dependency, (ii) are provinces other than Hubei mostly driven by export cases from Hubei and therefore follow a similar functional form in case counts as suggested by preliminary studies [10][11][12], or, alternatively, (iii) is the scaling law a consequence of endogeneous and basic epidemiological processes and a consequence of a balance between transmission events and containment factors.…”

Control Strategies to Curtail Transmission of COVID-19

“…Moreover, to minimise mortality rate of COVID-19, 3 u control variable is taken which helps to reduce critically infected cases by taking extra medical care of infected individuals. 4 u and 5 u control variables are taken to improve hospitalisation facility for infected and critically infected individuals respectively.…”

“…Moreover, the figure also demonstrates which control can be applied at how much intensity to control COVID-19 outbreak in seven weeks. The high fluctuation in 3 u control variable at an initial stage suggests that it is very important to control infected individuals to move at critical stage to reduce mortality due to COVID-19. And, this can be achieved easily if an infected individual gets proper vaccination for this disease.…”