[C20] Infectious Diseases

[C20-03] Dynamics of epidemic models with multiple latent or infectious stages on lattice space

*Kazunori Sato¹ (1. Shizuoka University (Japan))

Keywords:

lattice model,latent or infectious period,Erlang distribution,final size of epidemics,pair approximation

One of the concerns of the epidemiological modelling by differential equations is that latent or infectious periods follow exponential distributions. However, infectious diseases usually have specific latent or infectious periods. An introduction of multiple latent or infectious stages is a frequently used way to solve this unrealistic modelling, which leads to a total latent or infectious periods as Erlang distributions instead of exponential. Seminal works by Bailey [1] and Anderson and Watson [2] showed that final size of epidemics is not dependent on the number of latent or infectious stages for SEIR model, despite the fact that for multiple latent or infectious stages (1) the number of infected individuals in the path on susceptible-infected plane becomes larger and (2) the infected population more rapidly grows and a shorter epidemic occurs [3]. In contrast to these results, Matsumoto and Takasu [4] revealed that SIR model as spatial point process gives larger final size of epidemics for larger number of infectious stages by Monte Carlo simulation. Here we consider SIS, SIR, SEIS, SIRS, SEIR, SEIRS lattice models, and show that the number of latent or infectious stages does not affect equilibrium fractions of infected individuals and basic reproduction number R0 when once infected individuals can become susceptible again, such as SIS, SEIS, SIRS, SEIRS models. On the other hand, both SIR and SEIR models have larger final size of epidemics and larger basic reproduction number for larger number of latent or infectious stages. These results are obtained by Monte Carlo simulation on large scale of lattice space, and supported by pair approximation.

References
[1] N.T.J. Bailey, Some stochastic models for small epidemics in large populations, Appl.Statist. 13: 9-19, 1964.
[2] D. Anderson and R. Watson, On the spread of a disease with gamma distributed latent and infectious periods, Biometrika 67: 191-198, 1980.
[3] H.J. Wearing, P. Rohani and M.J. Keeling, Approximate models for the management of infectious diseases, PLoS Med. 2: e174, 2005.
[4] M. Matsumoto and F. Takasu, Extensions of SIR models to point pattern dynamics - Infection spread and the distribution of infection period, ESJ69, 2022.