Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time Heterogeneity

By Horst R. Thieme. SIAM Journal on Applied Mathematics, 2009

591 citations recorded by the source corpus.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/de41cbb61983cb6b5076b7d6a91e6bec1bd33268

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In Genetics

1. Xiao-Qiang Zhao
2. Xing Liang
3. Xingfu Zou
4. Yixiang Wu
5. Lei Zhang
6. Bin-Guo Wang
7. Feng-Bin Wang
8. Yu Huang

In Modeling and Simulation

1. Xiao-Qiang Zhao
2. Xing Liang
3. Lei Zhang
4. Feng-Bin Wang
5. Xingfu Zou
6. Bin-Guo Wang
7. Yu Huang
8. Yixiang Wu

In Public Health, Environmental and Occupational Health

1. Xiao-Qiang Zhao
2. Xing Liang
3. Xingfu Zou
4. Lei Zhang
5. Feng-Bin Wang
6. Yixiang Wu
7. Bin-Guo Wang
8. Yu Huang

Citations in the corpus

• Reproduction numbers of infectious disease models (2017, background): “If the range of K is one dimensional, then ℛ0 is the unique non-zero eigenvalue; see Diekmann et al. (2012, Section 7.4) for some examples, and see Section 4 in Thieme (2009) for discussion of an SIR model with variable susceptibility.”
• Dynamics and profiles of a diffusive host–pathogen system with distinct dispersal rates (2018, background): “, [11,21,23,25,26], which is closely related to the stability of E0.”
• Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models (2012, unknown): “Recently, Thieme [34] developed a general theory of spectral bound and reproduction number for the infinite-dimensional population structure and time heterogeneity.”
• Global dynamics of a PDE in-host viral model (2014, result): “By the general results in [26] and [15, Theorem 2.”
• Dynamics of a host-pathogen system on a bounded spatial domain (2015, unknown): “Applying the abstract results in Thieme [32], we conclude that the local stability of the disease-free equilibrium is also determined by the sign of R0−1 (see Lemma 2.”
• Basic Reproduction Ratios for Almost Periodic Compartmental Epidemic Models (2013, methodology): “As a consequence of the theory developed in [23], we have the following observation.”
• The construction of next-generation matrices for compartmental epidemic models (2010, background): “The proof originally given in Diekmann & Heesterbeek (2000) is incomplete, as pointed out in Thieme (2009; H. R. Thieme 2009, personal communication).”
• Basic Reproduction Ratios for Periodic Abstract Functional Differential Equations (with Application to a Spatial Model for Lyme Disease) (2017, background): “The theory in [34] can be applied to autonomous reaction-diffusionmodelswith orwithout time-delay (see, e.”