網絡傳播動力學

When a single drop of paint is dropped on a surface the amount of space that the drop will cover depends both on time and space. A short amount of time will no be enough for the drop to cover a greater area, and a small surface will bound the surface that the paint can cover. The same rules could be applied to a variety of phenomena, mixing chemicals, bacterial growth, or the spread of ideas or even the spread of infectious diseases. Although there exists a huge amount of research on the modeling of infectious diseases, the application of simple rules can offer some insights and easy interpretability on how a disease could spread.

當將一滴油漆滴在表面上時，該滴將覆蓋的空間量取決于時間和空間。 短時間不足以使液滴覆蓋更大的區域，而小的表面將束縛油漆可以覆蓋的表面。 相同的規則可以應用于多種現象，包括化學物質混合，細菌生長，思想傳播甚至傳染病傳播。 盡管存在大量關于傳染病建模的研究，但簡單規則的應用可以為疾病的傳播提供一些見識并易于解釋。

Let’s assume the following, an unknown disease is spreading through time and space in a population. Each square dot represents an individual, a black square represents an individual without the pathogen and a withe square represents an individual with the pathogen. Each frame represents a time step and each time step is equal to the time needed for an individual to spread the disease. As a novel disease, the amount of infected individuals is minimal. Each susceptible individual on the population will be affected by four surrounding neighbors. Those neighbors could be infected or uninfected. And for an individual to be infected there is a minimum of infected neighbors needed to infect the individual.

讓我們假設以下情況，一種未知的疾病正在人口中隨時間和空間傳播。 每個正方形點代表一個個體，黑色正方形代表沒有病原體的個體，而帶有正方形的方塊代表有病原體的個體。 每個幀代表一個時間步長，每個時間步長等于個體傳播疾病所需的時間。 作為一種新型疾病，受感染個體的數量很少。 人口中的每個易感個體都將受到周圍四個鄰居的影響。 那些鄰居可能被感染或未被感染。 對于一個要被感染的個體，感染該個體所需的感染鄰居最少。

By changing the number of infected neighbors needed to infect an individual a series of scenarios can be evaluated. Under the first couple of scenarios where the individual needs to be surrounded by four, three, or two infected neighbors the infection is unable to spread.

通過更改感染個人所需的被感染鄰居的數量，可以評估一系列情況。 在前兩個場景中，個人需要被四個，三個或兩個受感染的鄰居包圍，感染無法傳播。

However, when only one infected individual is needed to spread the pathogen a dramatic increase in the infected population can be seen. Different clusters of infection can be observed through time and after some time those clusters start to merge.

但是，當只需要一個被感染的個體來傳播病原體時，可以看到感染人口的急劇增加。 隨著時間的流逝，可以觀察到不同的感染群，一段時間后這些群開始合并。

Under the previous scenarios, about 0.01% of the population carries the pathogen in a secluded area. Increasing the number of infected populations to about 1% a similar pattern is observed. When the individual can be infected only when is surrounded by two three or four infected neighbors the infection is unable to spread. However, in some cases, the infection does not disappear but stays in small clusters of infected populations.

在以前的情況下，約有0.01％的人口將病原體攜帶在一個僻靜的地區。 將感染種群的數量增加到大約1％，可以觀察到類似的模式。 只有在被兩個三個或四個感染鄰居包圍的情況下，個體才能被感染，這種感染無法傳播。 但是，在某些情況下，感染并不會消失，而是停留在感染人群的小群中。

When only one neighbor is needed to infect an individual, the infection spreads dramatically. And almost instantaneously the pathogen can infect the entire population.

當只需要一個鄰居來感染一個人時，感染就會Swift蔓延。 而且，病原體幾乎可以瞬間感染整個人群。

To this point, it appears that the only scenario where the infection spreads through the population is when the pathogen can infect an individual when only one infected neighbor is needed to propagate the disease. And how rapidly the infection spread is proportional to the initial number of the infected population. Let’s see if that last assumption holds, now an evenly spaced number of infected individuals will be placed over the grid and evaluate the spread of the pathogen.

在這一點上，似乎感染在人群中蔓延的唯一情況是當只需要一個被感染的鄰居來傳播疾病時，病原體就可以感染一個人。 感染傳播的速度與感染人口的初始數量成正比。 讓我們看看最后一個假設是否成立，現在將等間隔分布的受感染個體放在網格上并評估病原體的傳播。

Under those constraints, it appears that an evenly spaced grid is not able to infect the entire population but reach an equilibrium. Looks like the randomness involved in how the individuals carry the pathogen helps its spread.

在這些約束下，似乎間隔均勻的網格無法感染整個種群，但可以達到平衡。 看起來個體攜帶病原體的方式所涉及的隨機性有助于其傳播。

Previous simulations exemplify how a pathogen can propagate through space and time. However, with an outbreak of a new disease, a common governmental intervention taken through an outbreak of an unknown disease is the restriction of social mobility, closing economic activities, restricting travel, and putting the population under quarantine. Social distancing is enforced as a measure to return to economic and social activities. Let’s enforce social distancing by adding a grid where there are no individuals available to propagate the disease.

先前的模擬例證了病原體如何在時空中傳播。 但是，隨著新疾病的爆發，通過未知疾病的爆發而采取的一項政府共同干預措施是限制社會流動性，結束經濟活動，限制出行并將人口隔離。 強制執行社會疏離措施，以恢復經濟和社會活動。 讓我們通過在沒有個人可以傳播疾病的地方添加一個網格來加強社會疏遠。

Gray lines represents a physical barrier orempty space.灰線表示物理屏障空白空間。

By applying those constrains a series of isolated clusters of infected individuals can be seen under every simulation configuration. Those results can show some resemblance to what can be happening at restaurants, cinemas, or some other establishments with large gatherings of people. If some of the people attending those establishments have the pathogen, the pathogen will be unable to spread trough its neighbors by simply applying social distancing. Diminishing the number of people that can be close together depletes the pathogen capacity to spread.

通過應用這些約束，可以在每種模擬配置下看到一系列隔離的感染個體簇。 這些結果可能與在餐館，電影院或其他人群聚集的其他場所可能發生的情況相似。 如果在這些機構中的某些人患有病原體，則僅通過社會隔離即可使病原體無法通過鄰居傳播。 減少可以靠近的人的數量會耗盡病原體的傳播能力。

The previous simulations are based on the two-dimensional cellular automata. With four neighbors and one individual in the middle, also known as the five neighbors two-dimensional automata. One of the most famous examples of two-dimensional automata is the one proposed by John Horton Conway also known as the game of life. The complete code to perform the previous simulations can be found in my GitHub by clicking here. See you in the next one.

先前的模擬基于二維細胞自動機。 在中間有四個鄰居和一個人，也稱為五個鄰居二維自動機。 二維自動機最著名的例子之一就是約翰·霍頓·康威(John Horton Conway)提出的例子，也被稱為生活游戲。 單擊此處，可以在我的GitHub中找到執行先前模擬的完整代碼。 下一個見。

翻譯自: https://medium.com/@octaviogl69/spread-dynamics-by-simple-rules-c3ad74c4c728

網絡傳播動力學

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