Chapter. 1. Evolutionary Virus Pandemics: From modeling and Simulations to Society -- Chapter. 2. Development and Analysis of Multiscale Models for Tuberculosis: From Molecules to Populations -- Chapter. 3. The use of crowd models for risk analysis during the Covid-19 pandemic -- Chapter. 4. Modeling household effects in epidemics -- Chapter. 5. An analytic look at the last pandemic’s spread and its control by decision-makers -- Chapter. 6. A time-dependent SIRD nonlinear cross-diffusion dpidemic model: Multiscale derivation and computational analysis -- Chapter. 7. Optimal control of an epidemic using compartmental models and measure differential equations -- Chapter. 8. Complex network approaches for epidemic modeling: a case study of COVID-19 -- Chapter. 9. How vaccination helps to relax the population mobility: an agent-based model approach.

In an increasingly globally-connected world, the ability to predict, monitor, and contain pandemics is essential to ensure the health and well-being of all. This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19. Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general. Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the societal level, the level of individuals, and the level of virus particles and the immune system. Chapters in this volume explore the latest research related to these items to demonstrate the utility of a variety of mathematical methods. Perspectives for the future are also offered.