Textbook in PDF format

Due to current circumstances (pandemic) involving the spread of a virus (SARS-COV-2) in a population, understanding the concepts and mechanisms used in deterministic models, associated with the description of the epidemic dynamics of a virus transmission in a community, has become of paramount importance in public policies to combat the pandemic, taking into account how intervention measures such as social distance, mask use, quarantine and vaccination are embedded in these mathematical models. The entire understanding of the epidemic dynamics is based on mathematical models by class of individuals (SIR or SEIR) whose study leads us to define a crucial magnitude for its understanding, known as the reproductive number (average number of people that an contaminated person infects until the end of the infectious period). Therefore, the objective of this work is to thoroughly investigate the epidemiological concepts implicit in the reproductive number (basic/effective) and its application when constructing possible scenarios involving the community transmission of a virus. First, we will present the main aspects of the SIR and SEIR models when describing an epidemic dynamics analytically. Next, we will calculate the effective reproductive number from the number of confirmed cases in a specific macro-region, monitored by a regional health agency, by the idea of serial interval and distributions (log-normal) and alternatively by the concept of linear regression and duplication time. Continuing, we will present solutions of the SIR and SEIR models numerically, complementing the analytical investigation. Finally, we will apply all the experience acquired in the previous discussions in the construction of an epidemic scenario for a specific micro-region.
Keywords: Quantitative Biology, Epidemiology, Deterministic Compartmental Models, Dynamics of Social Systems, Collective Phenomena, Data Analysis, Physics
Introductory Concepts
Epidemic Dynamics Described by the SIR Model
Influences (External/Internal) on Epidemic Dynamics and Intervention Measures
Social Distancing or Herd Immunity
Use of Masks and Hand Washing
Quarantine
Vaccination
Epidemic Dynamics Described by the SEIR Model
Predictions Determined by the Reproductive Number
Linear Regression
Solving Differential Equations via Numerical Methods
Searching for an Epidemic Scenario for the City
Final Reflections
Acknowledgements
Appendix: SIR and SEIR Models in Programming Language