Abstract
This paper explores the COVID19 transmission pattern and circulation dynamics in the Euclidean space at the lower peninsula of Michigan by using the divergence and curl concept in vector field. The COVID19 transmission volume flux can be calculated for each county by using vector divergence. The results shows Wayne county had the highest divergence (162660), the Kent county had the second highest divergence (152540), and the Saginaw county had the third highest divergence (103240), the divergence is positive which means the COVID19 virus was transmitted from these counties to other places. The results also shows Monroe county had the lowest divergence (-187843), the Allegan county had the second lowest number in divergence (-90824), the divergence is negative which means the COVID19 virus was transmitted from other places to these counties. The circulation of the virus is also calculated by using vector curl. The positive curl means that the virus has circulated in a counter-clockwise direction, and the negative curl means the virus has circulated in a clockwise direction.
 
 The divergence is an operator of the COVID19 transmission vector field, which produces a scalar field giving the quantity of the transmission vector field’s source at each location. The COVID19 spreading volume density of the outward flux of transmission field is represented by divergence around a given location. 
 
 The curl is an operator of the COVID19 transmission field, which describes the circulation of a transmission vector field. The curl at a location in COVID19 transmission field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a transmission field is formally defined as the circulation density at each location of COVID19 transmission field.
Highlights
1.1 Introduce the ProblemIt was announced by the World Health Organization (WHO) that COVID19 was first localized in Wuhan, Hubei Province, China in December, 2019, and it has been a significant human threat to the public health around the globe.As of April 8, 2021 globally, there have been about 0.135 billion confirmed case, and about 2.9 million reported deaths (WorldOMeters, 2021)
This paper explores the COVID19 transmission pattern and circulation dynamics in the Euclidean space at the lower peninsula of Michigan by using the divergence and curl concept in vector field
The COVID19 transmission volume flux can be calculated for each county by using vector divergence
Summary
As of April 8, 2021 globally, there have been about 0.135 billion confirmed case, and about 2.9 million reported deaths (WorldOMeters, 2021). In the U.S.A., there are about 31.7 million confirmed cases, and about 0.57 million reported deaths (WorldOMeters, 2021). In the state of Michigan, there are about 804,031confirmed cases and about 17,450 reported death at the time author wrote this paper (Michigan Department of Health, 2021). The dynamics of the spreading and transmission of the COVID19 around the globe are still complicated to explain. Many researchers have developed mathematics models attempting to describe the dynamics of the characteristics of a novel disease reigns.
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