Abstract
The aim of this short note is twofold. First, we formulate the general Kermack-McKendrick epidemic model incorporating static heterogeneity and show how it simplifies to a scalar Renewal Equation (RE) when separable mixing is assumed. A key general feature is that all information about the heterogeneity is encoded in one nonlinear real valued function of a real variable. Next, we specialize the model ingredients so that we can study the efficiency of mask wearing as a non-pharmaceutical intervention to reduce the spread of an infectious disease. Our main result affirms that the best way to protect the population as a whole is to protect yourself. This qualitative insight was recently derived in the context of an SIR network model. Here, we extend the conclusion to proportionate mixing models incorporating a general function describing expected infectiousness as a function of time since infection.
| Original language | English |
|---|---|
| Pages (from-to) | 17661-17671 |
| Number of pages | 11 |
| Journal | Mathematical Biosciences and Engineering |
| Volume | 20 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 15 Sept 2023 |
Bibliographical note
Publisher Copyright:© 2023 the Author(s)
Funding
It is a pleasure to thank Joan Saldaña and his team for organizing the stimulating Current Challenges Workshop on Epidemic Modelling, Girona 2023, and to thank Romualdo Pastor-Satorras for his inspiring lecture during the workshop. We are grateful to several referees and to Horst Thieme for feedback that helped to improve the exposition.
Keywords
- epidemic model
- heterogeneity
- Kermack-McKendrick
- mask efficiency
- separable mixing
