Stochastic modeling: The impact of chance
Stochastic modeling: The impact of chance
This chapter defines a stochastic counterpart to the homogeneous deterministic epidemic model introduced in Chapter 1. The model considers a homogeneous community of individuals that mix uniformly, meaning that there is no social structure in the community. The word “mix” is used in the sense of engaging in a type of contact that may possibly lead to transmission; what mixing is will therefore depend on characteristics of the infectious agent and the host. The randomness in the model stems from the latency and infectious periods being random (i.e., typically different for different individuals), and also from the contact process: infectious contacts of infected individuals occur randomly in time and with randomly selected individuals in a finite population. The chapter highlights two special cases, called the “general” epidemic and the Reed–Frost epidemic in the literature.
Keywords: infectious disease, stochastic epidemic model, general epidemic, Reed–Frost epidemic, homogeneous community
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