Mathematical epidemiology of infectious diseases: an ongoing challenge

2025/05/02 by Diekmann, Odo, Inaba, Hisashi, Thieme, Horst R. · 1 citation
#45G10 #45M20 #47J05 #92D25 #92D30 #FOS: Biological sciences #Populations and Evolution (q-bio.PE)

paper · doi:10.48550/arxiv.2505.01621

Abstract

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.

Citations

• Bistability and complex bifurcation diagrams generated by waning and boosting of immunity
• Epidemic outbreaks in structured host populations
• A Kermack--McKendrick type epidemic model with double threshold phenomenon (and a possible application to Covid-19)
• Basic concepts for the Kermack and McKendrick model with static heterogeneity
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• A data analysis of women's trails among ICM speakers
• A class of abstract delay differential equations in the light of suns and stars. II
• The Mathematics of Infectious Diseases
• On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations

Cited by

• Age-Structured Population Dynamics

Related

• The Mathematics of Infectious Diseases
• Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus
• A model with exposure in the epidemiological sense. Part 1 -- Base model
• Basic stochastic transmission models and their inference
• Reaction-Diffusion Systems in Epidemiology