On the use of the geometric approach to global stability for three dimensional ODE systems: A bilinear case

In this paper, we consider a general bilinear three dimensional ODE system, whose structure generalizes many mathematical models of biological interest, including many from epidemics. Our main goal is to find sufficient conditions, expressed in terms of the parameters of the system, ensuring that the geometric approach to global stability analysis, due to [M.Y. Li, J.S. Muldowney, A geometric approach to global-stability problems, SIAM J. Math. Anal. 27 (4) (1996) 1070-1083], may be successfully applied. We completely determine the dynamics of the general system, including thresholds and global stability of the nontrivial equilibrium. The obtained result is applied to several epidemic models. We further show how the role of new parameters on stability of well-established models may be emphasized.     

Effect of prey growth and predator cannibalism rate on the stability of a structured population model

The dynamics of a structured population model including cannibalism is analyzed. Hopf bifurcation threshold for the cannibalistic attack rate is detected. Linear and nonlinear stability analysis through the Lyapunov Direct Method is also provided. The effects of relevant parameters on the stability are discussed. In particular, cannibalism is found to have a stabilizing effect, whereas the prey growth effect is opposite. The result is emphasized by numerical simulations.     

On a possible mechanism for Ar 4 + fragmentation

The full potential energy surface (PES) for the collinear Ar ₄ ⁺ cluster as a function of the three internuclear distances is computed at the post-Hartree-Fock level using Density Functional Theory (DFT) methods to treat dynamic correlation effects. The behaviour of the overall configuration energy minima as the central Ar ₂ ⁺ bond stretches is analysed as a function of the fragmentation coordinates of the wing atoms. The coupling between the stretching coordinate and the fragmentation coordinates is also analysed over the whole PES. The calculations suggest that large vibrational energy content in the core dimer ion causes localization of the coupling with either wing atoms which could in turn favour energetically the sequential fragmentation, while Ar ₄ ⁺ with a vibrationally cold core markedly lowers any energy barrier to fragment in a concerted fashion. Such suggestions provide further useful information for what has been found in some of the experimental studies on this ionic system (and on larger ionized argon clusters) and underline the possible role which the internal vibrational energy content of the ionic cluster can play in the fragmentation.     

Cephem-Pyrazinoic Acid Conjugates: Circumventing Resistance in Mycobacterium tuberculosis

Tuberculosis (TB) is a leading source of infectious disease mortality globally. Antibiotic-resistant strains comprise an estimated 10 % of new TB cases and present an urgent need for novel therapeutics. β-lactam antibiotics have traditionally been ineffective against M. tuberculosis (Mtb), the causative agent of TB, due to the organism's inherent expression of β-lactamases that destroy the electrophilic β-lactam warhead. We have developed novel β-lactam conjugates, which exploit this inherent β-lactamase activity to achieve selective release of pyrazinoic acid (POA), the active form of a first-line TB drug. These conjugates are selectively active against M. tuberculosis and related mycobacteria, and activity is retained or even potentiated in multiple resistant strains and models. Preliminary mechanistic investigations suggest that both the POA “warhead” as well as the β-lactam “promoiety” contribute to the observed activity, demonstrating a codrug strategy with important implications for future TB therapy.     

Effects of information-dependent vaccination behavior on coronavirus outbreak: insights from a SIRI model

A mathematical model is proposed to assess the effects of a vaccine on the time evolution of a coronavirus outbreak. The model has the basic structure of SIRI compartments (susceptible–infectious–recovered–infectious) and is implemented by taking into account of the behavioral changes of individuals in response to the available information on the status of the disease in the community. We found that the cumulative incidence may be significantly reduced when the information coverage is high enough and/or the information delay is short, especially when the reinfection rate is high enough to sustain the presence of the disease in the community. This analysis is inspired by the ongoing outbreak of a respiratory illness caused by the novel coronavirus COVID-19.

     

Modeling the Influence of Public’s Memory on the Corruption–Popularity Dilemma in Politics

We consider the problem of a rational politician who gains benefit from both being popular and corrupt. In 1994, Feichtinger and Wirl studied this trade-off by means of an infinite-horizon optimal control approach. We reconsider the problem over a finite time horizon, to model the dilemma of a politician who stays in office for a limited period of time and wishes to be reelected. We also include explicitly the possibility that awareness of politician’s conduct to the general population is delayed and the effect of such delay on the politician’s optimal behavior is analyzed. We show the outcomes under several different scenarios, with particular reference to the role of the politician’s communication skills. One general conclusion is that the synergy of a good public’s memory and immediate knowledge of corruption may often help the people to protect themselves from political corruption. Moreover, this synergy may greatly enhance the popularity of a politician with poor communication skills, provided that he/she aims at maximizing benefit from popularity during his/her mandate.     

Experimental study of high energy electron interactions in a superconducting aluminum alloy resonant bar

Peak amplitude measurements of the fundamental mode of oscillation of a suspended aluminum alloy bar hit by an electron beam show that the amplitude is enhanced by a factor ∼3.5 when the material is in the superconducting state. This result is consistent with the cosmic ray observations performed by the resonant gravitational wave detector NAUTILUS, made of the same alloy, when operated in the superconducting state. A comparison of the experimental data with the predictions of the model describing the underlying physical process is also presented.     

Fragmentation dynamics of ionized argon clusters: an effective potential model

A dynamical model based on an effective potential is employed to describe metastability and the related time scales for evaporation processes in ionized Argon clusters (Ar) _n ⁺ , withn from 6 up to 27. The effective interaction, and its dependence on the cluster size, is obtained by combining previous ab initio results and Monte Carlo simulations for the above systems with an assumed linear variation of the cluster volume with then number of monomers. The overall metastability of the excited clusters is linked to the possible local rotational ‘temperature’ of such species and the distributions of the ensuing lifetimes are analysed as function of cluster size and of different nucleation mechanisms. It is found that an unusually large range of lifetime values is obtained from the present modelling, in general accord with earlier experiments, and that the existence of large rotational barriers can markedly delay the dissociation of metastable species.