Advancing Epidemic Research: Interdisciplinary Approaches and Innovative Modeling Techniques

Dear Colleagues,

COVID-19 has posed an unprecedented challenge to the global scientific community, emphasizing the need to study epidemic phenomena through interdisciplinary approaches to address emerging difficulties. These challenges include developing mathematical compartmental models to simulate the virus's spread and evaluating the effectiveness of interventions such as social distancing, lockdowns, and vaccination campaigns. In addition, data analysis and visualization are essential for monitoring the pandemic's progress, identifying patterns and trends, and effectively communicating findings to the public and policymakers.

Innovative modelling approaches enhance our understanding and prediction of the virus's spread. These techniques include:

1. Agent-based models: simulating the interactions of individuals within a population based on their characteristics, behaviors, and movement patterns, these models provide a granular understanding of transmission dynamics and the potential impact of interventions.
2. Network models: representing populations as networks with nodes and edges, network models capture the heterogeneous nature of human contact patterns and can be used to identify critical nodes for targeted interventions or study the impact of social network structures on disease spread.
3. Metapopulation models: dividing the population into smaller subpopulations connected by travel or migration, metapopulation models account for the spatial heterogeneity of disease transmission and the impact of travel restrictions on the virus's spread.
4. Data-driven models: Incorporating real-time data such as mobility patterns, social media activity, and healthcare system capacity, these models offer more accurate predictions and adapt to changing conditions. Machine learning and artificial intelligence techniques can further improve model predictions by identifying hidden patterns in data.
5. Stochastic models: by incorporating randomness, these models account for uncertainty and variability in disease transmission and provide a range of possible outcomes, aiding decision-makers to understand the uncertainty associated with different scenarios.

In this Special Issue, we focus on the research contributions to numerical optimization, numerical parameter estimation, dynamic modelling, and neural networks, which have been instrumental in enhancing our understanding and prediction of the virus's spread.

Numerical Optimization: mathematical models used to study epidemics often involve complex optimization problems to identify the best intervention strategies or allocate resources effectively.

Numerical Parameter Estimation: accurately estimating crucial epidemiological parameters, such as transmission rates, infection probabilities, and recovery rates, is vital for reliable epidemic modelling.

Dynamic Modeling: Dynamic models, such as ordinary differential equations (ODEs) and partial differential equations (PDEs), have been widely used to describe epidemics' temporal and spatial evolution. Using fractional calculus, both temporal derivatives and fractional Laplacians allow introducing memory effects in models, almost analogous to accounting for hereditary phenomena with "Volterra" memory integrals in Fick's constitutive law.

Neural Networks: artificial neural networks, particularly deep learning techniques, have been employed to model complex epidemic processes, forecast disease spread, and evaluate intervention strategies.

These innovative approaches have advanced our understanding of the COVID-19 pandemic and paved the way for future research on epidemics.

In this Special Issue, we aim to emphasize how these techniques and methodologies, alongside other innovative approaches used by scholars from different disciplinary backgrounds, contribute to a turning point in the study of epidemic phenomena. Our goal is to provide an up-to-date overview of state-of-the-art research on epidemic phenomena, highlighting the importance of interdisciplinary contributions and the innovations spurred by the experience of COVID-19.

Prof. Fabiana Zama
Prof. Franca Franchi
Prof. Germana Landi
Prof. Elena Loli Piccolomini
Guest Editors

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• mathematical modeling of epidemic diseases
• cross-diffusion
• multiscale problems
• Turing instability
• pattern formation
• fractional calculus
• numerical parameter estimation
• dynamic modeling
• neural networks
• infectious disease control
• interdisciplinary approaches