How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks

With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic considerations and provide a theoretical result on the probability of the extinction of the disease. Based on this calibration, we explore the variability in disease spread by stochastic simulations. In particular, we demonstrate how important epidemic indices change as a function of the contagiousness of the disease and the connectivity of the network. Our results quantify the role of starting node degree in determining these indices, commonly used to describe epidemic spread.Comment: 22 pages, 9 figure

A geometric analysis of the SIRS compartmental model with fast information and misinformation spreading

We propose an SIRS compartmental model with demography and fast information and misinformation spreading in the population. The analysis of the complete 6-dimensional system shows the existence of seven equilibrium points. Since under our assumptions the system evolves on two time scales, we completely characterize the possible asymptotic behaviours with techniques of Geometric Singular Perturbation Theory (GSPT). During our analysis of the fast dynamics, we identify three branches of the critical manifold, which exist under determined conditions. We perform a theoretical bifurcation analysis of the fast system to understand the relation between these three equilibria when varying specific parameters of the fast system. We then observed a delayed loss of stability on the various branches of the critical manifold, as the slow dynamics may cause the branches to lose their hyperbolicity. We emphasise how the inclusion of (mis)information spreading, even in low dimensional compartmental models, can radically alter the asymptotic behaviour of the epidemic. We conclude with numerical simulations of various remarkable scenarios.Comment: 27 pages, 8 figures, 1 tabl

A geometric analysis of the SIRS model with secondary infections

We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria of the system and analyze their stability. We find conditions for the existence of two endemic equilibria, for some cases in which $\mathcal{R}_0 < 1$. Then, we unravel the interplay of the three time scales, providing conditions to foresee whether the system evolves in all three scales, or only in the fast and the intermediate ones. We conclude with numerical simulations and bifurcation analysis, to complement our analytical results.Comment: 31 pages, 9 figure

A survey on Lyapunov functions for epidemic compartmental models

In this survey, we propose an overview on Lyapunov functions for a variety of compartmental models in epidemiology. We exhibit the most widely employed functions, and provide a commentary on their use. Our aim is to provide a comprehensive starting point to readers who are attempting to prove global stability of systems of ODEs. The focus is on mathematical epidemiology, however some of the functions and strategies presented in this paper can be adapted to a wider variety of models, such as prey–predator or rumor spreading

A geometric analysis of the impact of large but finite switching rates on vaccination evolutionary games

In contemporary society, social networks accelerate decision dynamics causing a rapid switch of opinions in a number of fields, including the prevention of infectious diseases by means of vaccines. This means that opinion dynamics can nowadays be much faster than the spread of epidemics. Hence, we propose a Susceptible-Infectious-Removed epidemic model coupled with an evolutionary vaccination game embedding the public health system efforts to increase vaccine uptake. This results in a global system ``epidemic model + evolutionary game''. The epidemiological novelty of this work is that we assume that the switching to the strategy ``pro vaccine'' depends on the incidence of the disease. As a consequence of the above-mentioned accelerated decisions, the dynamics of the system acts on two different scales: a fast scale for the vaccine decisions and a slower scale for the spread of the disease. Another, and more methodological, element of novelty is that we apply Geometrical Singular Perturbation Theory (GSPT) to such a two-scale model and we then compare the geometric analysis with the Quasi-Steady-State Approximation (QSSA) approach, showing a criticality in the latter. Later, we apply the GSPT approach to the disease prevalence-based model already studied in (Della Marca and d'Onofrio, Comm Nonl Sci Num Sim, 2021) via the QSSA approach by considering medium-large values of the strategy switching parameter.Comment: 26 pages, 6 figure

Plexin-B1 plays a redundant role during mouse development and in tumour angiogenesis

<p>Abstract</p> <p>Background</p> <p>Plexins are a large family of transmembrane receptors for the Semaphorins, known for their role in the assembly of neural circuitry. More recently, Plexins have been implicated in diverse biological functions, including vascular growth, epithelial tissue morphogenesis and tumour development. In particular, PlexinB1, the receptor for Sema4D, has been suggested to play a role in neural development and in tumour angiogenesis, based on in vitro studies. However, the tissue distribution of PlexinB1 has not been extensively studied and the functional relevance of this receptor in vivo still awaits experimental testing. In order to shed light on PlexinB1 function in vivo, we therefore undertook the genomic targeting of the mouse gene to obtain loss of function mutants.</p> <p>Results</p> <p>This study shows that PlexinB1 receptor and its putative ligand, Sema4D, have a selective distribution in nervous and epithelial tissues during development and in the adult. PlexinB1 and Sema4D show largely complementary cell distribution in tissues, consistent with the idea that PlexinB1 acts as the receptor for Sema4D in vivo. Interestingly, PlexinB1 is also expressed in certain tissues in the absence of Sema4D, suggesting Sema4D independent activities. High expression of PlexinB1 was found in lung, kidney, liver and cerebellum.</p> <p>Mutant mice lacking expression of semaphorin receptor PlexinB1 are viable and fertile. Although the axon collapsing activity of Sema4D is impaired in PlexinB1 deficient neurons, we could not detect major defects in development, or in adult histology and basic functional parameters of tissues expressing PlexinB1. Moreover, in the absence of PlexinB1 the angiogenic response induced by orthotopically implanted tumours was not affected, suggesting that the expression of this semaphorin receptor in endothelial cells is redundant.</p> <p>Conclusion</p> <p>Our expression analysis suggests a multifaceted role of PlexinB1 during mouse development and tissue homeostasis in the adult. Nonetheless, the genetic deletion of PlexinB1 does not result in major developmental defects or clear functional abnormalities. We infer that PlexinB1 plays a redundant role in mouse development and it is not strictly required for tumour induced angiogenesis.</p

Optimized EGFR blockade strategies in <i>EGFR</i> addicted gastroesophageal adenocarcinomas

Purpose: Gastric and gastroesophageal adenocarcinomas represent the third leading cause of cancer mortality worldwide. Despite significant therapeutic improvement, the outcome of patients with advanced gastroesophageal adenocarcinoma is poor. Randomized clinical trials failed to show a significant survival benefit in molecularly unselected patients with advanced gastroesophageal adenocarcinoma treated with anti-EGFR agents.Experimental Design: We performed analyses on four cohorts: IRCC (570 patients), Foundation Medicine, Inc. (9,397 patients), COG (214 patients), and the Fondazione IRCCS Istituto Nazionale dei Tumori (206 patients). Preclinical trials were conducted in patient-derived xenografts (PDX).Results: The analysis of different gastroesophageal adenocarcinoma patient cohorts suggests that EGFR amplification drives aggressive behavior and poor prognosis. We also observed that EGFR inhibitors are active in patients with EGFR copy-number gain and that coamplification of other receptor tyrosine kinases or KRAS is associated with worse response. Preclinical trials performed on EGFR-amplified gastroesophageal adenocarcinoma PDX models revealed that the combination of an EGFR mAb and an EGFR tyrosine kinase inhibitor (TKI) was more effective than each monotherapy and resulted in a deeper and durable response. In a highly EGFR-amplified nonresponding PDX, where resistance to EGFR drugs was due to inactivation of the TSC2 tumor suppressor, cotreatment with the mTOR inhibitor everolimus restored sensitivity to EGFR inhibition.Conclusions: This study underscores EGFR as a potential therapeutic target in gastric cancer and identifies the combination of an EGFR TKI and a mAb as an effective therapeutic approach. Finally, it recognizes mTOR pathway activation as a novel mechanism of primary resistance that can be overcome by the combination of EGFR and mTOR inhibitors