Multiple pandemic waves vs multi-period/multi-phasic epidemics: Global shape of the COVID-19 pandemic.

The overall course of the COVID-19 pandemic in Western countries has been characterised by complex sequences of phases. In the period before the arrival of vaccines, these phases were mainly due to the alternation between the strenghtening/lifting of social distancing measures, with the aim to balance the protection of health and that of the society as a whole. After the arrival of vaccines, this multi-phasic character was further emphasised by the complicated deployment of vaccination campaigns and the onset of virus' variants. To cope with this multi-phasic character, we propose a theoretical approach to the modeling of overall pandemic courses, that we term multi-period/multi-phasic, based on a specific definition of phase. This allows a unified and parsimonious representation of complex epidemic courses even when vaccination and virus' variants are considered, through sequences of weak ergodic renewal equations that become fully ergodic when appropriate conditions are met. Specific hypotheses on epidemiological and intervention parameters allow reduction to simple models. The framework suggest a simple, theory driven, approach to data explanation that allows an accurate reproduction of the overall course of the COVID-19 epidemic in Italy since its beginning (February 2020) up to omicron onset, confirming the validity of the concept.

Computational validation of clonal and subclonal copy number alterations from bulk tumor sequencing using CNAqc.

Copy number alterations (CNAs) are among the most important genetic events in cancer, but their detection from sequencing data is challenging because of unknown sample purity, tumor ploidy, and general intra-tumor heterogeneity. Here, we present CNAqc, an evolution-inspired method to perform the computational validation of clonal and subclonal CNAs detected from bulk DNA sequencing. CNAqc is validated using single-cell data and simulations, is applied to over 4000 TCGA and PCAWG samples, and is incorporated into the validation process for the clinically accredited bioinformatics pipeline at Genomics England. CNAqc is designed to support automated quality control procedures for tumor somatic data validation.

A Bayesian method to infer copy number clones from single-cell RNA and ATAC sequencing.

Single-cell RNA and ATAC sequencing technologies enable the examination of gene expression and chromatin accessibility in individual cells, providing insights into cellular phenotypes. In cancer research, it is important to consistently analyze these states within an evolutionary context on genetic clones. Here we present CONGAS+, a Bayesian model to map single-cell RNA and ATAC profiles onto the latent space of copy number clones. CONGAS+ clusters cells into tumour subclones with similar ploidy, rendering straightforward to compare their expression and chromatin profiles. The framework, implemented on GPU and tested on real and simulated data, scales to analyse seamlessly thousands of cells, demonstrating better performance than single-molecule models, and supporting new multi-omics assays. In prostate cancer, lymphoma and basal cell carcinoma, CONGAS+ successfully identifies complex subclonal architectures while providing a coherent mapping between ATAC and RNA, facilitating the study of genotype-phenotype maps and their connection to genomic instability.

Multiple epidemic waves as the outcome of stochastic SIR epidemics with behavioral responses: a hybrid modeling approach.

In the behavioral epidemiology (BE) of infectious diseases, little theoretical effort seems to have been devoted to understand the possible effects of individuals' behavioral responses during an epidemic outbreak in small populations. To fill this gap, here we first build general, behavior implicit, SIR epidemic models including behavioral responses and set them within the framework of nonlinear feedback control theory. Second, we provide a thorough investigation of the effects of different types of agents' behavioral responses for the dynamics of hybrid stochastic SIR outbreak models. In the proposed model, the stochastic discrete dynamics of infection spread is combined with a continuous model describing the agents' delayed behavioral response. The delay reflects the memory mechanisms with which individuals enact protective behavior based on past data on the epidemic course. This results in a stochastic hybrid system with time-varying transition probabilities. To simulate such system, we extend Gillespie's classic stochastic simulation algorithm by developing analytical formulas valid for our classes of models. The algorithm is used to simulate a number of stochastic behavioral models and to classify the effects of different types of agents' behavioral responses. In particular this work focuses on the effects of the structure of the response function and of the form of the temporal distribution of such response. Among the various results, we stress the appearance of multiple, stochastic epidemic waves triggered by the delayed behavioral response of individuals.

Testing a simple and frugal model of health protective behaviour in epidemic times.

The COVID-19 epidemic highlighted the necessity to integrate dynamic human behaviour change into infectious disease transmission models. The adoption of health protective behaviour, such as handwashing or staying at home, depends on both epidemiological and personal variables. However, only a few models have been proposed in the recent literature to account for behavioural change in response to the health threat over time. This study aims to estimate the relevance of TELL ME, a simple and frugal agent-based model developed following the 2009 H1N1 outbreak to explain individual engagement in health protective behaviours in epidemic times and how communication can influence this. Basically, TELL ME includes a behavioural rule to simulate individual decisions to adopt health protective behaviours. To test this rule, we used behavioural data from a series of 12 cross-sectional surveys in France over a 6-month period (May to November 2020). Samples were representative of the French population (N = 24,003). We found the TELL ME behavioural rule to be associated with a moderate to high error rate in representing the adoption of behaviours, indicating that parameter values are not constant over time and that other key variables influence individual decisions. These results highlight the crucial need for longitudinal behavioural data to better calibrate epidemiological models accounting for public responses to infectious disease threats.

J-SPACE: a Julia package for the simulation of spatial models of cancer evolution and of sequencing experiments.

BACKGROUND: The combined effects of biological variability and measurement-related errors on cancer sequencing data remain largely unexplored. However, the spatio-temporal simulation of multi-cellular systems provides a powerful instrument to address this issue. In particular, efficient algorithmic frameworks are needed to overcome the harsh trade-off between scalability and expressivity, so to allow one to simulate both realistic cancer evolution scenarios and the related sequencing experiments, which can then be used to benchmark downstream bioinformatics methods. RESULT: We introduce a Julia package for SPAtial Cancer Evolution (J-SPACE), which allows one to model and simulate a broad set of experimental scenarios, phenomenological rules and sequencing settings.Specifically, J-SPACE simulates the spatial dynamics of cells as a continuous-time multi-type birth-death stochastic process on a arbitrary graph, employing different rules of interaction and an optimised Gillespie algorithm. The evolutionary dynamics of genomic alterations (single-nucleotide variants and indels) is simulated either under the Infinite Sites Assumption or several different substitution models, including one based on mutational signatures. After mimicking the spatial sampling of tumour cells, J-SPACE returns the related phylogenetic model, and allows one to generate synthetic reads from several Next-Generation Sequencing (NGS) platforms, via the ART read simulator. The results are finally returned in standard FASTA, FASTQ, SAM, ALN and Newick file formats. CONCLUSION: J-SPACE is designed to efficiently simulate the heterogeneous behaviour of a large number of cancer cells and produces a rich set of outputs. Our framework is useful to investigate the emergent spatial dynamics of cancer subpopulations, as well as to assess the impact of incomplete sampling and of experiment-specific errors. Importantly, the output of J-SPACE is designed to allow the performance assessment of downstream bioinformatics pipelines processing NGS data. J-SPACE is freely available at: https://github.com/BIMIB-DISCo/J-Space.jl .

A behavioural modelling approach to assess the impact of COVID-19 vaccine hesitancy.

We introduce a compartmental epidemic model to describe the spread of COVID-19 within a population, assuming that a vaccine is available, but vaccination is not mandatory. The model takes into account vaccine hesitancy and the refusal of vaccination by individuals, which take their decision on vaccination based on both the present and past information about the spread of the disease. Theoretical analysis and simulations show that voluntary vaccination can certainly reduce the impact of the disease but is unable to eliminate it. We also demonstrate how the information-related parameters affect the dynamics of the disease. In particular, vaccine hesitancy and refusal are better contained in case of widespread information coverage and short-term memory. Finally, the possible impact of seasonality on the spread of the disease is investigated.

Feedback control of social distancing for COVID-19 via elementary formulae.

Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields elementary closed-form formulae for open-loop social distancing scenarios, where, for instance, the increase of the number of uninfected people may be taken into account. Those formulae might therefore be useful to decision makers. A feedback loop stemming from model-free control leads to a remarkable robustness with respect to severe uncertainties and mismatches. Although an identification procedure is presented, a good knowledge of the recovery rate is not necessary for our control strategy.

Dynamics of partially mitigated multi-phasic epidemics at low susceptible depletion: phases of COVID-19 control in Italy as case study.

To mitigate the harmful effects of the COVID-19 pandemic, world countries have resorted - though with different timing and intensities - to a range of interventions. These interventions and their relaxation have shaped the epidemic into a multi-phase form, namely an early invasion phase often followed by a lockdown phase, whose unlocking triggered a second epidemic wave, and so on. In this article, we provide a kinematic description of an epidemic whose time course is subdivided by mitigation interventions into a sequence of phases, on the assumption that interventions are effective enough to prevent the susceptible proportion to largely depart from 100% (or from any other relevant level). By applying this hypothesis to a general SIR epidemic model with age-since-infection and piece-wise constant contact and recovery rates, we supply a unified treatment of this multi-phase epidemic showing how the different phases unfold over time. Subsequently, by exploiting a wide class of infectiousness and recovery kernels allowing reducibility (either to ordinary or delayed differential equations), we investigate in depth a low-dimensional case allowing a non-trivial full analytical treatment also of the transient dynamics connecting the different phases of the epidemic. Finally, we illustrate our theoretical results by a fit to the overall Italian COVID-19 epidemic since March 2020 till February 2021 i.e., before the mass vaccination campaign. This show the abilities of the proposed model in effectively describing the entire course of an observed multi-phasic epidemic with a minimal set of data and parameters, and in providing useful insight on a number of aspects including e.g., the inertial phenomena surrounding the switch between different phases.

Evidence of disorientation towards immunization on online social media after contrasting political communication on vaccines. Results from an analysis of Twitter data in Italy.

BACKGROUND: In Italy, in recent years, vaccination coverage for key immunizations as MMR has been declining to worryingly low levels, with large measles outbreaks. As a response in 2017, the Italian government expanded the number of mandatory immunizations introducing penalties to unvaccinated children's families. During the 2018 general elections campaign, immunization policy entered the political debate with the government in-charge blaming oppositions for fuelling vaccine scepticism. A new government (formerly in the opposition) established in 2018 temporarily relaxed penalties and announced the introduction of forms of flexibility. OBJECTIVES AND METHODS: First, we supplied a definition of disorientation, as the "lack of well-established and resilient opinions among individuals, therefore causing them to change their positions as a consequence of sufficient external perturbations". Second, procedures for testing for the presence of both short and longer-term collective disorientation in Twitter signals were proposed. Third, a sentiment analysis on tweets posted in Italian during 2018 on immunization topics, and related polarity evaluations, were used to investigate whether the contrasting announcements at the highest political level might have originated disorientation amongst the Italian public. RESULTS: Vaccine-relevant tweeters' interactions peaked in response to main political events. Out of retained tweets, 70.0% resulted favourable to vaccination, 16.4% unfavourable, and 13.6% undecided, respectively. The smoothed time series of polarity proportions exhibit frequent large changes in the favourable proportion, superimposed to a clear up-and-down trend synchronized with the switch between governments in Spring 2018, suggesting evidence of disorientation among the public. CONCLUSIONS: The reported evidence of disorientation for opinions expressed in online social media shows that critical health topics, such as vaccination, should never be used to achieve political consensus. This is worsened by the lack of a strong Italian institutional presence on Twitter, calling for efforts to contrast misinformation and the ensuing spread of hesitancy. It remains to be seen how this disorientation will impact future parents' vaccination decisions.

Spatio-temporal games of voluntary vaccination in the absence of the infection: the interplay of local versus non-local information about vaccine adverse events.

Under voluntary vaccination, a critical role in shaping the level and trends of vaccine uptake is played by the type and structure of information that is received and used by parents of children eligible for vaccination. In this article we investigate the feedbacks of spatial mobility and the spatial structure of information on vaccination dynamics, by extending to a continuous spatially structured setting existing behavioral epidemiology models for the impact of vaccine adverse events (VAEs) on vaccination choices. We considered the simplest spatial setting, namely classical 'Fickian' diffusion, and focused on the noteworthy case where the infection is absent. This scenario mimics the important case of a population where a previously endemic vaccine preventable infection was successfully eliminated, but the re-emergence of the disease must be prevented. This is, for example, the case of poliomyelitis in most countries worldwide. In such a situation, the dynamics of VAEs and of the related information arguably become the key determinant of vaccination decision and of collective coverage. In relation to this 'information issue', we compared the effects of three main cases: (i) purely local information, where agents react only to locally occurred events; (ii) a mix of purely local and global, country-wide, information due e.g., to country-wide media and the internet; (iii) a mix of local and non-local information. By representing these different information options through a range of different spatial information kernels, we investigated: the presence and stability of space-homogeneous, nontrivial, behavior-induced equilibria; the existence of bifurcations; the existence of classical and generalized traveling waves; and the effects of awareness campaigns enacted by the Public Health System to sustain vaccine uptake. Finally, we analyzed some analogies and differences between our models and those of the Theory of Innovation Diffusion.

Optimal time-profiles of public health intervention to shape voluntary vaccination for childhood diseases.

In order to seek the optimal time-profiles of public health systems (PHS) Intervention to favor vaccine propensity, we apply optimal control (OC) to a SIR model with voluntary vaccination and PHS intervention. We focus on short-term horizons, and on both continuous control strategies resulting from the forward-backward sweep deterministic algorithm, and piecewise-constant strategies (which are closer to the PHS way of working) investigated by the simulated annealing (SA) stochastic algorithm. For childhood diseases, where disease costs are much larger than vaccination costs, the OC solution sets at its maximum for most of the policy horizon, meaning that the PHS cannot further improve perceptions about the net benefit of immunization. Thus, the subsequent dynamics of vaccine uptake stems entirely from the declining perceived risk of infection (due to declining prevalence) which is communicated by direct contacts among parents, and unavoidably yields a future decline in vaccine uptake. We find that for relatively low communication costs, the piecewise control is close to the continuous control. For large communication costs the SA algorithm converges towards a non-monotone OC that can have oscillations.

Optimal public health intervention in a behavioural vaccination model: the interplay between seasonality, behaviour and latency period.

Hesitancy and refusal of vaccines preventing childhood diseases are spreading due to 'pseudo-rational' behaviours: parents overweigh real and imaginary side effects of vaccines. Nonetheless, the 'Public Health System' (PHS) may enact public campaigns to favour vaccine uptake. To determine the optimal time profiles for such campaigns, we apply the optimal control theory to an extension of the susceptible-infectious-removed (SIR)-based behavioural vaccination model by d'Onofrio et al. (2012, PLoS ONE, 7, e45653). The new model is of susceptible-exposed-infectious-removed (SEIR) type under seasonal fluctuations of the transmission rate. Our objective is to minimize the total costs of the disease: the disease burden, the vaccination costs and a less usual cost: the economic burden to enact the PHS campaigns. We apply the Pontryagin minimum principle and numerically explore the impact of seasonality, human behaviour and latency rate on the control and spread of the target disease. We focus on two noteworthy case studies: the low (resp. intermediate) relative perceived risk of vaccine side effects and relatively low (resp. very low) speed of imitation. One general result is that seasonality may produce a remarkable impact on PHS campaigns aimed at controlling, via an increase of the vaccination uptake, the spread of a target infectious disease. In particular, a higher amplitude of the seasonal variation produces a higher effort and this, in turn, beneficially impacts the induced vaccine uptake since the larger is the strength of seasonality, the longer the vaccine propensity remains large. However, such increased effort is not able to fully compensate the action of seasonality on the prevalence.

Special issue on Erice 'MathCompEpi 2015' Proceedings.

The mathematical and computational modelling of the spread of infectious diseases is a research field in applied mathematics that in the same time was both able to give an impetum to various areas of the dynamical systems theory and mathematical analysis, and to give an important contribution to the biological and epidemiological understanding of the spread of these diseases. National as well as Inter-National health authorities adopt routinely in the practice methodologies and concept that were born in the field of Mathematical and Computational Epidemiology (MCE) for assisting public Health decisions and policies. A major example is provided by the huge advancement in modelling and prediction on pandemic threats, and related preparedness plans for disease containment/mitigation. This operative influence in biomedicine is unparalleled in any other fields of mathematical and computational biology, with the possible exception of intra-host virus dynamics, whose models partly derive from those of MCE.

Effect of seasonality on the dynamics of an imitation--based vaccination model with public health intervention.

We extend here the game-theoretic investigation made by d'Onofrio et al (2012) on the interplay between private vaccination choices and actions of the public health system (PHS) to favor vaccine propensity in SIR-type diseases. We focus here on three important features. First, we consider a SEIR--type disease. Second, we focus on the role of seasonal fluctuations of the transmission rate. Third, by a simple population--biology approach we derive - with a didactic aim - the game theoretic equation ruling the dynamics of vaccine propensity, without employing 'economy--related' concepts such as the payoff. By means of analytical and analytical--approximate methods, we investigate the global stability of the of disease--free equilibria. We show that in the general case the stability critically depends on the `shape' of the periodically varying transmission rate. In other words, the knowledge of the average transmission rate (ATR) is not enough to make inferences on the stability of the elimination equilibria, due to the presence of the class of latent subjects. In particular, we obtain that the amplitude of the oscillations favors the possible elimination of the disease by the action of the PHS, through a threshold condition. Indeed, for a given average value of the transmission rate, in absence of oscillations as well as for moderate oscillations, there is no disease elimination. On the contrary, if the amplitude exceeds a threshold value, the elimination of the disease is induced. We heuristically explain this apparently paradoxical phenomenon as a beneficial effect of the phase when the transmission rate is under its average value: the reduction of transmission rate (for example during holidays) under its annual average over--compensates its increase during periods of intense contacts. We also investigate the conditions for the persistence of the disease. Numerical simulations support the theoretical predictions. Finally, we briefly investigate the qualitative behavior of the non--autonomous system for SIR--type disease, by showing that the stability of the elimination equilibria are, in such a case, determined by the ATR.

Global stability of infectious disease models with contact rate as a function of prevalence index.

In this paper, we consider a SEIR epidemiological model with information--related changes in contact patterns. One of the main features of the model is that it includes an information variable, a negative feedback on the behavior of susceptible subjects, and a function that describes the role played by the infectious size in the information dynamics. Here we focus in the case of delayed information. By using suitable assumptions, we analyze the global stability of the endemic equilibrium point and disease--free equilibrium point. Our approach is applicable to global stability of the endemic equilibrium of the previously defined SIR and SIS models with feedback on behavior of susceptible subjects.

Erratum: Spatiotemporal bounded noises and transitions induced by them in solutions of the real Ginzburg-Landau model [Phys. Rev. E 86, 021118 (2012)].

This corrects the article DOI: 10.1103/PhysRevE.86.021118.

Maps and atlases of cancer mortality: a review of a useful tool to trigger new questions.

In this review we illustrate our view on the epidemiological relevance of geographically mapping cancer mortality. In the first part of this work, after delineating the history of cancer mapping with a view on interpretation of Cancer Mortality Atlases, we briefly illustrate the 'art' of cancer mapping. Later we summarise in a non-mathematical way basic methods of spatial statistics. In the second part of this paper, we employ the 'Atlas of Cancer Mortality in the European Union and the European Economic Area 1993-1997' in order to illustrate spatial aspects of cancer mortality in Europe. In particular, we focus on the cancer related to tobacco and alcohol epidemics and on breast cancer which is of particular interest in cancer mapping. Here we suggest and reiterate two key concepts. The first is that a cancer atlas is not only a visual tool, but it also contain appropriate spatial statistical analyses that quantify the qualitative visual impressions to the readers even though at times revealing fallacy. The second is that a cancer atlas is by no means a book where answers to questions can be found. On the contrary, it ought to be considered as a tool to trigger new questions.

The role of stochastic gene switching in determining the pharmacodynamics of certain drugs: basic mechanisms.

In this paper we analyze the impact of the stochastic fluctuation of genes between their ON and OFF states on the pharmacodynamics of a potentially large class of drugs. We focus on basic mechanisms underlying the onset of in vitro experimental dose-response curves, by investigating two elementary molecular circuits. Both circuits consist in the transcription of a gene and in the successive translation into the corresponding protein. Whereas in the first the activation/deactivation rates of the single gene copy are constant, in the second the protein, now a transcription factor, amplifies the deactivation rate, so introducing a negative feedback. The drug is assumed to enhance the elimination of the protein, and in both cases the success of therapy is assured by keeping the level of the given protein under a threshold for a fixed time. Our numerical simulations suggests that the gene switching plays a primary role in determining the sigmoidal shape of dose-response curves. Moreover, the simulations show interesting phenomena related to the magnitude of the average gene switching time and to the drug concentration. In particular, for slow gene switching a significant fraction of cells can respond also in the absence of drug or with drug concentrations insufficient for the response in a deterministic setting. For higher drug concentrations, the non-responding fraction exhibits a maximum at intermediate values of the gene switching rates. For fast gene switching, instead, the stochastic prediction follows the prediction of the deterministic approximation, with all the cells responding or non-responding according to the drug dose.