Stochastic Modeling of an Infectious Disease, Part I: Understand the Negative Binomial Distribution and Predict an Epidemic More Reliably

by   Hisashi Kobayashi, et al.

Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts often grossly wrong, concerning the numbers of people who get infected or die? The purpose of this study is to better understand the stochastic nature of an epidemic disease, and answer the above questions. Much of the work on infectious diseases has been based on "SIR deterministic models," (Kermack and McKendrick:1927.) We will explore stochastic models that can capture the essence of the seemingly erratic behavior of an infectious disease. A stochastic model, in its formulation, takes into account the random nature of an infectious disease. The stochastic model we study here is based on the "birth-and-death process with immigration" (BDI for short), which was proposed in the study of population growth or extinction of some biological species. The BDI process model ,however, has not been investigated by the epidemiology community. The BDI process is one of a few birth-and-death processes, which we can solve analytically. Its time-dependent probability distribution function is a "negative binomial distribution" with its parameter r less than 1. The "coefficient of variation" of the process is larger than √(1/r) > 1. Furthermore, it has a long tail like the zeta distribution. These properties explain why infection patterns exhibit enormously large variations. The number of infected predicted by a deterministic model is much greater than the median of the distribution. This explains why any forecast based on a deterministic model will fail more often than not.


page 1

page 2

page 3

page 4


Stochastic Modeling of an Infectious Disease Part III-A: Analysis of Time-Nonhomogeneous Models

We extend our BDI (birth-death-immigration) process based stochastic mod...

Comparing the Behaviour of Deterministic and Stochastic Model of SIS Epidemic

Studies about epidemic modelling have been conducted since before 19th c...

A Multi-Stage Stochastic Programming Approach to Epidemic Resource Allocation with Equity Considerations

Existing compartmental models in epidemiology are limited in terms of op...

Epidemics on Hypergraphs: Spectral Thresholds for Extinction

Epidemic spreading is well understood when a disease propagates around a...

Expected Time to Extinction of SIS Epidemic Model Using Quasy Stationary Distribution

We study that the breakdown of epidemic depends on some parameters, that...

Exploration of the effects of epidemics on the regional socio-economics: a modelling approach

Pandemics, in addition to affecting the health of populations, can have ...

Please sign up or login with your details

Forgot password? Click here to reset