This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called 2 2. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focussed also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.

Cancer results from a complex interplay of different biological, chemical, and physical phenomena that span a wide range of time and length scales. Computational modeling may help to unfold the role of multiple evolving factors that exist and interact in the tumor microenvironment. Understanding these complex multiscale interactions is a crucial step towards predicting cancer growth and in developing effective therapies. We integrate different modeling approaches in a multiscale, avascular, hybrid tumor growth model encompassing tissue, cell, and sub-cell scales. At the tissue level, we consider the dispersion of nutrients and growth factors in the tumor microenvironment, which are modeled through reaction-diffusion equations. At the cell level, we use an agent based model (ABM) to describe normal and tumor cell dynamics, with normal cells kept in homeostasis and cancer cells differentiated apoptotic, hypoxic, and necrotic states. Cell movement is driven by the balance of a variety of forces according to Newton's second law, including those related to growth-induced stresses. Phenotypic transitions are defined by specific rule of behaviors that depend on microenvironment stimuli. We integrate in each cell/agent a branch of the epidermal growth factor receptor (EGFR) pathway. This pathway is modeled by a system of coupled nonlinear differential equations involving the mass laws of 20 molecules. The rates of change in the concentration of some key molecules trigger proliferation or migration advantage response. The bridge between cell and tissue scales is built through the reaction and source terms of the partial differential equations. Our hybrid model is built in a modular way, enabling the investigation of the role of different mechanisms at multiple scales on tumor progression. This strategy allows representating both the collective behavior due to cell assembly as well as microscopic intracellular phenomena described by signal transduction pathways. Here, we investigate the impact of some mechanisms associated with sustained proliferation on cancer progression. Specifically, we focus on the intracellular proliferation/migration-advantage-response driven by the EGFR pathway and on proliferation inhibition due to accumulation of growth-induced stresses. Simulations demonstrate that the model can adequately describe some complex mechanisms of tumor dynamics, including growth arrest in avascular tumors. Both the sub-cell model and growth-induced stresses give rise to heterogeneity in the tumor expansion and a rich variety of tumor behaviors.

This paper presents general approaches for addressing some of the most important issues in predictive computational oncology concerned with developing classes of predictive models of tumor growth. First, the process of developing mathematical models of vascular tumors evolving in the complex, heterogeneous, macroenvironment of living tissue; second, the selection of the most plausible models among these classes, given relevant observational data; third, the statistical calibration and validation of models in these classes, and finally, the prediction of key Quantities of Interest (QOIs) relevant to patient survival and the effect of various therapies. The most challenging aspects of this endeavor is that all of these issues often involve confounding uncertainties: in observational data, in model parameters, in model selection, and in the features targeted in the prediction. Our approach can be referred to as "model agnostic" in that no single model is advocated; rather, a general approach that explores powerful mixture-theory representations of tissue behavior while accounting for a range of relevant biological factors is presented, which leads to many potentially predictive models. Then representative classes are identified which provide a starting point for the implementation of OPAL, the Occam Plausibility Algorithm (OPAL) which enables the modeler to select the most plausible models (for given data) and to determine if the model is a valid tool for predicting tumor growth and morphology (). All of these approaches account for uncertainties in the model, the observational data, the model parameters, and the target QOI. We demonstrate these processes by comparing a list of models for tumor growth, including reaction-diffusion models, phase-fields models, and models with and without mechanical deformation effects, for glioma growth measured in murine experiments. Examples are provided that exhibit quite acceptable predictions of tumor growth in laboratory animals while demonstrating successful implementations of OPAL.

Experiments have shown that wild type P. aeruginosa swarms much faster than rhlAB mutants on 0.4% agar concentration surface. These observations imply that development of a liquid thin film is an important component of the self-organized swarming process. A multiscale model is presented in this paper for studying interplay of key hydrodynamical and biological mechanisms involved in the swarming process of P. aeruginosa. This model combines a liquid thin film equation, convection-reaction-diffusion equations and a cell-based stochastic discrete model. Simulations demonstrate how self-organized swarming process based on the microscopic individual bacterial behavior results in complicated fractal type patterns at macroscopic level. It is also shown that quorum sensing mechanism causing rhamnolipid synthesis and resulting liquid extraction from the substrate lead to the fast swarm expansion. Simulations also demonstrate formation of fingers (tendrils) at the edge of a swarm which have been earlier observed in experiments.