Alberto d'Onofrio

Stability properties of pulse vaccination strategy in SEIR epidemic model

The problem of the applicability of the pulse vaccination strategy (PVS) for the stable eradication of some relevant general class of infectious diseases is analyzed in terms of study of local asymptotic stability (LAS) and global asymptotic stability (GAS) of the periodic eradication solution for the SEIR epidemic model in which is included the PVS. Demographic variations due or not to diseased-related fatalities are also considered. Due to the non-triviality of the Floquets matrix associate to the studied model, the LAS is studied numerically and in this way it is found a simple approximate (but analytical) sufficient criterion which is an extension of the LAS constraint for the stability of the trivial equilibrium in SEIR model without vaccination. The numerical simulations also seem to suggest that the PVS is slightly more efficient than the continuous vaccination strategy. Analytically, the GAS of the eradication solutions is studied and it is demonstrated that the above criteria for the LAS guarantee also the GAS.

Statistical physics of vaccination

Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination - one of the most important preventive measures of modern times - is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research.

A general framework for modeling tumor-immune system competition and immunotherapy : Mathematical analysis and biomedical inferences

Abstract In this work we propose and investigate a family of models, which admits as particular cases some well known mathematical models of tumor-immune system interaction, with the additional assumption that the influx of immune system cells may be a function of the number of cancer cells. Constant, periodic and impulsive therapies (as well as the non-perturbed system) are investigated both analytically for the general family and, by using the model by Kuznetsov et al. [V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor, A.S. Perelson, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, Bull. Math. Biol. (1994) 56(2) 295–321), via numerical simulations. Simulations seem to show that the shape of the function modeling the therapy is a crucial factor only for very high values of the therapy period T, whereas for realistic values of T, the eradication of the cancer cells depends on the mean values of the therapy term. Finally, some medical inferences are proposed.

On pulse vaccination strategy in the SIR epidemic model with vertical transmission

The aim of this short paper is to improve a result recently given by Lu et al. on the global asymptotic stability of the eradication solution of the PVS applied to diseases with vertical transmission, by demonstrating that the condition for local stability guarantees also the global stability.

Pulse vaccination strategy in the sir epidemic model: Global asymptotic stable eradication in presence of vaccine failures

In this paper, we study the use of a pulse vaccination strategy to eradicate infectious diseases modelizable by SIR epidemic model. We demonstrate the global asymptotic stability of the eradication solution (which was conjectured by Agur and coworkers in [1] for pulse vaccination in the classical SIR model) for a general model in which nonpermanent immunization, variations of the total population size, and the emerging problem of the vaccine failures are considered. As a strategy using a second inoculation is a standard practice, we propose a model to describe a modification of this strategy including the second inoculation and we study its local asymptotic stability.

On optimal delivery of combination therapy for tumors

A mathematical model for the scheduling of angiogenic inhibitors in combination with a chemotherapeutic agent is formulated. Conditions are given that allow tumor eradication under constant infusion therapies. Then the optimal scheduling of a vessel disruptive agent in combination with a cytotoxic drug is considered as an optimal control problem. Both theoretical and numerical results on the structure of optimal controls are presented.

Modeling the interplay between human behavior and the spread of infectious diseases

Modeling the interplay between human behavior and the spread of infectious diseases / , Modeling the interplay between human behavior and the spread of infectious diseases / , کتابخانه دیجیتال جندی شاپور اهواز

Delay-induced oscillatory dynamics of tumour-immune system interaction

The aim of this work on tumour-immune system (T-IS) interaction is to assess the effect of delays concerning the stimulation of the immune system by tumour cells, as well as the interplay between antitumour immunotherapies and delays. After defining a new family of super-macroscopic models for the T-IS interaction, we introduce a constant delay in the proliferation of immune effectors. We then investigate, both analytically and by means of simulations, the stability of equilibria and the onset of sustained oscillations through Hopf bifurcations. Both constant and exponentially distributed lags are considered. In particular, in the case of periodically varying immunotherapies we show that nonlinear resonances and chaos may arise, although for parameters slightly outside the range of biological realism.

A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy.

In this paper we propose a class of models that describe the mutual interaction between tumour growth and the development of tumour vasculature and that generalize existing models. The study is mainly focused on the effect of a therapy that induces tumour vessel loss (anti-angiogenic therapy), with the aim of finding conditions that asymptotically guarantee the eradication of the disease under constant infusion or periodic administration of the drug. Furthermore, if tumour and/or vessel dynamics exhibit time delays, we derive conditions for the existence of Hopf bifurcations. The destabilizing effect of delays on achieving the tumour eradication is also investigated. Finally, global conditions for stability and eradication in the presence of delays are given for some particular cases.

Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times

In this paper we study the use of a pulse vaccination strategy to eradicate infectious diseases modelable by epidemic model having gamma distributed infectious and latent time. We demonstrate the global asymptotic stability of the eradication solution for a general model in which co-presence of a continuous vaccination strategy, the non-permanent duration of the immunization and the emerging problem of the vaccine failures are considered.