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Hisashi Inaba

Publications and source records attributed to Hisashi Inaba.

5 recordsLinked to original sources
arXiv2025

A mathematical model of human population reproduction through marriage

We develop a linear one-sex dynamical model of human population reproduction through marriage. In our model, a woman may marry and divorce multiple times; however, only women who are currently married are assumed to bear children. The iterative marriage process is formulated as a three-state compartmental model, which is described by a system of McKendrick equations with a marital birth rate function that depends on the duration of marriage and the age at marriage. To examine the impact of changing nuptiality on fertility, we derive new formulas for the reproduction indices. In particular, the total fertility rate (TFR) is expressed as the product of the total marriage number and the average total marital fertility. Using Japanese vital statistics, we show that our model provides a reasonable estimate of the current TFR and its future trajectory.

q-bio.PE↗
arXiv2025

Mathematical epidemiology of infectious diseases: an ongoing challenge

The aim of this paper is to present an, admittedly somewhat subjective, bird's eye view of the mathematical theory concerning the spread of an infectious disease in a susceptible host population with static structure, culminating in a future-oriented description of various modelling challenges.

q-bio.PE↗
arXiv2023

Basic concepts for the Kermack and McKendrick model with static heterogeneity

In this paper, we consider the infection-age-dependent Kermack--McKendrick model in which host individuals are distributed in a continuous state space. To provide a mathematical foundation for the heterogeneous model, we develop a $L^1$-framework to formulate basic epidemiological concepts. First, we show the mathematical well-posedness of the basic model under appropriate conditions allowing the unbounded parameters with non-compact domain. Next we define the basic reproduction number and prove the pandemic threshold theorem. We then present a systematic procedure to compute the effective reproduction number and the herd immunity threshold. Finally we give some illustrative examples and concrete results by using the separable mixing assumption.

q-bio.PE↗
arXiv2023

The effect of host population heterogeneity on epidemic outbreaks

In the first part of this paper, we review old and new results about the influence of host population heterogeneity on (various characteristics of) epidemic outbreaks. In the second part we highlight a modelling issue that so far has received little attention: how do contact patterns, and hence transmission opportunities, depend on the size and the composition of the host population? Without any claim on completeness, we offer a range of potential (quasi-mechanistic) submodels. The overall aim of the paper is to describe the state-of-the-art and to catalyse new work.

q-bio.PE↗