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A Brief Theory of Epidemic Kinetics

機譯：流行病動力學簡論

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In the context of the COVID-19 epidemic, and on the basis of the Theory of Dynamical Systems, we propose a simple theoretical approach for the expansion of contagious diseases, with a particular focus on viral respiratory tracts. The infection develops through contacts between contagious and exposed people, with a rate proportional to the number of contagious and of non-immune individuals, to contact duration and turnover, inversely proportional to the efficiency of protection measures, and balanced by the average individual recovery response. The obvious initial exponential increase is readily hindered by the growing recovery rate, and also by the size reduction of the exposed population. The system converges towards a stable attractor whose value is expressed in terms of the “reproductive rate” , depending on contamination and recovery factors. Various properties of the attractor are examined, and particularly its relations with . Decreasing this ratio below a critical value leads to a tipping threshold beyond which the epidemic is over. By contrast, significant values of the above ratio may bring the system through a bifurcating hierarchy of stable cycles up to a chaotic behaviour.
機譯：在COVID-19流行的背景下，并在動力系統(tǒng)理論的基礎(chǔ)上，我們提出了一種擴展傳染性疾病的簡單理論方法，尤其著重于病毒性呼吸道。感染是通過接觸有傳染力的人和接觸者而發(fā)展的，感染率與傳染性和非免疫性個體的數(shù)量成正比，與接觸的持續(xù)時間和周轉(zhuǎn)率成正比，與保護措施的效率成反比，并由平均個體恢復反應平衡。明顯的初始指數(shù)增加很容易被恢復率的增長以及暴露人群的大小減少所阻礙。該系統(tǒng)趨于穩(wěn)定的吸引子，其價值取決于污染和恢復因素，以“繁殖率”表示。研究了吸引子的各種特性，尤其是與的關(guān)系。將該比率降低到臨界值以下會導致臨界閾值，超過該閾值流行病就結(jié)束了。相比之下，上述比率的顯著值可能會使系統(tǒng)經(jīng)歷穩(wěn)定周期的分叉層次，直至出現(xiàn)混亂的行為。

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