We use topological data analysis and machine learning to study a seminal model of collective motion in biology [M. R. D’Orsogna et al., Phys. Rev. Lett. 96, 104302 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive social forces and gives rise to collective behaviors such as flocking and milling. To classify the emergent collective motion in a large library of numerical simulations and to recover model parameters from the simulation data, we apply machine learning techniques to two different types of input. First, we input time series of order parameters traditionally used in studies of collective motion. Second, we input measures based on topology that summarize the time-varying persistent homology of simulation data over multiple scales. This topological approach does not require prior knowledge of the expected patterns. For both unsupervised and supervised machine learning methods, the topological approach outperforms the one that is based on traditional order parameters.

The role of vaccine success is introduced into an epidemic spreading model consisting ofthree states: susceptible, infectious, and vaccinated. Moreover, the effect of threetypes, namely, contact, local, and global, of infection awareness and immunizationawareness is also taken into consideration. The model generalizes those considered inPastor-Satorras and Vespignani [Phys. Rev. E 63, 066117 (2001)],Pastor-Satorras and Vespignani [Phys. Rev. E 65, 036104 (2002)], Morenoet al. [Eur. Phys. J. B 26, 521–529 (2002)], Wu etal. [Chaos 22, 013101 (2012)], and Wu et al.[Chaos 24, 023108 (2014)]. Our main results contain the following. First, theepidemic threshold is explicitly obtained. In particular, we show that, for any initialconditions, the epidemic eventually dies out regardless of what other factors are wheneversome type of immunization awareness is considered, and vaccination has a perfect success.Moreover, the threshold is independent of the global type of awareness. Second, we comparethe effect of contact and local types of awareness on the epidemic thresholds betweenheterogeneous networks and homogeneous networks. Specifically, we find that the epidemicthreshold for the homogeneous network can be lower than that of the heterogeneous networkin an intermediate regime for intensity of contact infection awareness while it is higherotherwise. In summary, our results highlight the important and crucial roles of bothvaccine success and contact infection awareness on epidemic dynamics.

Robustness describes the capacity for a biological system to remain canalized despiteperturbation. Genetic robustness affords maintenance of phenotype despite mutationalinput, necessarily involving the role of epistasis. Environmental robustness is phenotypicconstancy in the face of environmental variation, where epistasis may be uninvolved. Herewe discuss genetic and environmental robustness, from the standpoint of infectious diseaseevolution, and suggest that robustness may be a unifying principle for understanding howdifferent disease agents evolve. We focus especially on viruses with RNA genomes due totheir importance in the evolution of emerging diseases and as model systems to testrobustness theory. We present new data on adaptive constraints for a model RNA viruschallenged to evolve in response to UV radiation. We also draw attention to otherinfectious disease systems where robustness theory may prove useful for bridgingevolutionary biology and biomedicine, especially the evolution of antibiotic resistance inbacteria, immune evasion by influenza, and malaria parasite infections.