網(wǎng)絡(luò)傳播動(dòng)力學(xué)

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(dāng)將一滴油漆滴在表面上時(shí)，該滴將覆蓋的空間量取決于時(shí)間和空間。 短時(shí)間不足以使液滴覆蓋更大的區(qū)域，而小的表面將束縛油漆可以覆蓋的表面。 相同的規(guī)則可以應(yīng)用于多種現(xiàn)象，包括化學(xué)物質(zhì)混合，細(xì)菌生長(zhǎng)，思想傳播甚至傳染病傳播。 盡管存在大量關(guān)于傳染病建模的研究，但簡(jiǎn)單規(guī)則的應(yīng)用可以為疾病的傳播提供一些見(jiàn)識(shí)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(shè)以下情況，一種未知的疾病正在人口中隨時(shí)間和空間傳播。 每個(gè)正方形點(diǎn)代表一個(gè)個(gè)體，黑色正方形代表沒(méi)有病原體的個(gè)體，而帶有正方形的方塊代表有病原體的個(gè)體。 每個(gè)幀代表一個(gè)時(shí)間步長(zhǎng)，每個(gè)時(shí)間步長(zhǎng)等于個(gè)體傳播疾病所需的時(shí)間。 作為一種新型疾病，受感染個(gè)體的數(shù)量很少。 人口中的每個(gè)易感個(gè)體都將受到周圍四個(gè)鄰居的影響。 那些鄰居可能被感染或未被感染。 對(duì)于一個(gè)要被感染的個(gè)體，感染該個(gè)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(guò)更改感染個(gè)人所需的被感染鄰居的數(shù)量，可以評(píng)估一系列情況。 在前兩個(gè)場(chǎng)景中，個(gè)人需要被四個(gè)，三個(gè)或兩個(gè)受感染的鄰居包圍，感染無(wú)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(dāng)只需要一個(gè)被感染的個(gè)體來(lái)傳播病原體時(shí)，可以看到感染人口的急劇增加。 隨著時(shí)間的流逝，可以觀察到不同的感染群，一段時(shí)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(gè)僻靜的地區(qū)。 將感染種群的數(shù)量增加到大約1％，可以觀察到類似的模式。 只有在被兩個(gè)三個(gè)或四個(gè)感染鄰居包圍的情況下，個(gè)體才能被感染，這種感染無(wú)法傳播。 但是，在某些情況下，感染并不會(huì)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(dāng)只需要一個(gè)鄰居來(lái)感染一個(gè)人時(shí)，感染就會(huì)Swift蔓延。 而且，病原體幾乎可以瞬間感染整個(gè)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(diǎn)上，似乎感染在人群中蔓延的唯一情況是當(dāng)只需要一個(gè)被感染的鄰居來(lái)傳播疾病時(shí)，病原體就可以感染一個(gè)人。 感染傳播的速度與感染人口的初始數(shù)量成正比。 讓我們看看最后一個(gè)假設(shè)是否成立，現(xiàn)在將等間隔分布的受感染個(gè)體放在網(wǎng)格上并評(píng)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(wǎng)格無(wú)法感染整個(gè)種群，但可以達(dá)到平衡。 看起來(lái)個(gè)體攜帶病原體的方式所涉及的隨機(jī)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(shí)空中傳播。 但是，隨著新疾病的爆發(fā)，通過(guò)未知疾病的爆發(fā)而采取的一項(xiàng)政府共同干預(yù)措施是限制社會(huì)流動(dòng)性，結(jié)束經(jīng)濟(jì)活動(dòng)，限制出行并將人口隔離。 強(qiáng)制執(zhí)行社會(huì)疏離措施，以恢復(fù)經(jīng)濟(jì)和社會(huì)活動(dòng)。 讓我們通過(guò)在沒(méi)有個(gè)人可以傳播疾病的地方添加一個(gè)網(wǎng)格來(lái)加強(qiáng)社會(huì)疏遠(yuǎn)。

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(guò)應(yīng)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(gè)體簇。 這些結(jié)果可能與在餐館，電影院或其他人群聚集的其他場(chǎng)所可能發(fā)生的情況相似。 如果在這些機(jī)構(gòu)中的某些人患有病原體，則僅通過(guò)社會(huì)隔離即可使病原體無(wú)法通過(guò)鄰居傳播。 減少可以靠近的人的數(shù)量會(huì)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(xì)胞自動(dòng)機(jī)。 在中間有四個(gè)鄰居和一個(gè)人，也稱為五個(gè)鄰居二維自動(dòng)機(jī)。 二維自動(dòng)機(jī)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(zhí)行先前模擬的完整代碼。 下一個(gè)見(jiàn)。

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

網(wǎng)絡(luò)傳播動(dòng)力學(xué)

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