A Cybernetics-based Dynamic Infection Model for Analyzing SARS-COV-2 Infection Stability and Predicting Uncontrollable Risks

Wenlei Xiao; Qiang Liu; J Huan; Pengpeng Sun; Liuquan Wang; Chenxin Zang; Sanying Zhu; Liansheng Gao

There are major differences between the city Wuhan and other cities such as Shanghai, Beijing, etc. Firstly, Wuhan was facing a serious shortage of medical supplies against the outbreak of SARS-COV-2. Consequently, we designed an integral saturation module on the incubation bypass, whose capability is mostly limited by the total hospital beds; Secondly, since the original source of the coronavirus locates in Wuhan, the system input should be replaced with a spontaneous infection source; Thirdly, 5 million population had been exported outside Wuhan until Jan 23, 2020. The model should be supplemented by this emigration, as it took a large proportion of the total population (5 million left versus 9 million remained). For those sakes, Wuhan Model is designed as Fig. 6 . From the daily reported news, we collected all the numbers of hospital beds with dates, including those in designated, makeshift, Huoshenshan and Leishenshan hospitals. Those numbers of beds with dates were employed in the module, admission capability of hospitals, so that the dynamic consumption of medical resources could be emulated. The system input is replaced with a spontaneous infection source, which can be simplified as a unit impulse signal, while its exact date should be deduced from later confirmed infected cases. Until the city went into lockdown, emigration had exported a number of infected patients. The factor R 2 represents the infection rate at kth day of the city population M (k), which were decreasing iteratively and evenly by the daily emigration x 2 (k). The iterative formulas of R 2 (k) and M (k) are given as follow: