Modeling the spread of infectious diseases is central to the field of computational epidemiology. Two prominent approaches to modeling the contagion process include (i) simulating the spread in contact networks through Monte-Carlo processes and (ii) tracking the disease dynamics using meta-population models. In both cases, the individuals are explicitly (contact networks) or implicitly (meta-population) assumed to belong to exactly one disease state (e.g., susceptible, infected, etc.).

In reality, the disease states of individuals are rarely so cleanly compartmentalized. A particular agent can exist in multiple disease states (such as infected and exposed) concurrently with varying probability. To model this stochasticity, we present a new method, that we term as the Probabilistic Infection Model (PIM). Unlike traditional models that assign exactly one state to each agent at each time step, the PIM computes the probability of each agent being in each of the infectious states.

Our proposed PIM provides a more layered understanding of the dynamics of the outbreak at individual levels, by allowing the users to (i) estimate the value of R₀ at individual vertices and (ii) instead of an all or none value, provides the probability of each infected state of an agent. Additionally, using our probabilistic approach the overall trajectories of the outbreaks can be computed in one simulation, as opposed to the numerous (order of hundreds) repeated simulations required for the Monte Carlo process.

We demonstrate the efficacy of PIM by comparing the results of the PIM simulations with those obtained by simulating stochastic SEIR models, as well as the time required for the simulations. We present results at the system and at the individual levels for three diseases; measles and two strains of influenza. We demonstrate how the PIM can be used to study the effect of varying the transimissibility of COVID-19 on its outbreak.

This paper is an extended version of a manuscript published in the proceedings of the 2020 International Conference on Computational Science (ICCS)[30]. These extensions are primarily within Sections 4 (Relationship between graph structure and probability of infection) and 5 (Effect of varying COVID-19 transmissibility on outbreak dynamics).

传染病传播建模是计算流行病学领域的核心。对传染过程建模的两种主要方法包括 (i) 通过蒙特卡罗过程模拟接触网络中的传播和 (ii) 使用元种群模型跟踪疾病动态。在这两种情况下，个体被明确地（接触网络）或隐含地（元群体）假定为恰好属于一种疾病状态（例如，易感、感染等）。

实际上，个体的疾病状态很少如此清晰地划分。一种特定的病原体可以以不同的概率同时存在于多种疾病状态（例如感染和暴露）中。为了模拟这种随机性，我们提出了一种新方法，我们将其称为概率感染模型 (PIM)。与在每个时间步为每个代理指定一个状态的传统模型不同，PIM 计算每个代理处于每个感染状态的概率。

我们提出的 PIM 通过允许用户 (i) 估计单个顶点的R ₀值和 (ii) 而不是全或无值，提供对个体级别爆发动态的更分层理解代理的每个感染状态。此外，使用我们的概率方法，可以在一次模拟中计算爆发的整体轨迹，而不是蒙特卡洛过程所需的大量（数百个）重复模拟。

我们通过将 PIM 模拟的结果与通过模拟随机 SEIR 模型获得的结果以及模拟所需的时间进行比较来证明 PIM 的功效。我们在系统和个体层面上展示了三种疾病的结果；麻疹和两种流感病毒。我们展示了如何使用 PIM 来研究改变 COVID-19 的传播能力对其爆发的影响。

这篇论文是发表在 2020 年国际计算科学会议 (ICCS)[30] 论文集中的手稿的扩展版本。这些扩展主要在第 4 节（图结构与感染概率之间的关系）和第 5 节（不同 COVID-19 传播性对爆发动态的影响）中。