arXiv subjects

Rossella Della Marca

Publications and source records attributed to Rossella Della Marca.

8 recordsLinked to original sources

arXiv2026

Traveling fronts in a spatial epidemic model with slow loss of immunity

We investigate the emergence of traveling front solutions in a spatial SIRS epidemic model with diffusion acting on the infected population. The model exhibits a natural slow-fast structure due to the presence of a small parameter governing the loss of immunity, which induces a separation of scales in the dynamics. Using a traveling wave reduction, the PDE system is transformed into a singularly perturbed system of ODEs, which we analyze within the framework of Geometric Singular Perturbation Theory. In the singular limits, we study the fast excursions governed by the layer problem, and the slow evolution close to the critical manifold. In particular, we identify an entry-exit mechanism tracking the transitions between slow and fast regimes, and derive a quantitative characterization of the entry-exit dynamics. Numerical simulations of the full system confirm the validity of the proposed geometric picture. The traveling front is shown to consist of a concatenation of local, fast, and slow segments, in agreement with the theoretical analysis.

math.DS↗

arXiv2026

Impact of Nirsevimab prophylaxis on RSV dynamics: a stage-structured modelling study

Respiratory syncytial virus (RSV) is a leading cause of bronchiolitis and other lower respiratory tract infections in infants. Increased viral circulation in the post-COVID era and heterogeneous prevention strategies across regions have made RSV control more challenging. We develop a stage-structured, age-stratified Susceptible-Infected-Recovered (SIR) compartmental model tailored to the Italian setting to investigate the population-level impact of infant prophylaxis with Nirsevimab, a long-acting monoclonal antibody. Scenario-based simulations over a multi-year horizon show that increasing infant protection coverage substantially reduces RSV incidence among infants and also yields indirect benefits in older age groups. In particular, extending coverage to infants born outside the epidemic season further lowers cumulative incidence, although infant-targeted prophylaxis alone does not reduce the control reproduction number below the epidemic threshold in the parameter range explored. These findings suggest that broader and more consistent infant Nirsevimab coverage may reduce RSV burden and support the evaluation of alternative implementation strategies in the Italian context.

q-bio.PE↗

arXiv2026

Weakly nonlinear analysis of a reaction-diffusion model for demyelinating lesions in Multiple Sclerosis

Multiple Sclerosis is a chronic autoimmune disorder characterized by the degradation of the myelin sheath in the central nervous system, leading to neurological impairments. In this work, we analyze a reaction-diffusion model derived from kinetic theory to study the formation of demyelinating lesions. We perform a Turing instability analysis and a weakly nonlinear analysis to investigate different spatial patterns that may emerge. Our study examines how key parameters, including the squeezing probability of immune cells and the chemotactic response, impact pattern formation. Numerical simulations confirm the analytical results, revealing the emergence of distinct spatial structures.

q-bio.TO↗

arXiv2024

Information index augmented eRG to model vaccination behaviour: A case study of COVID-19 in the US

Recent pandemics triggered the development of a number of mathematical models and computational tools apt at curbing the socio-economic impact of these and future pandemics. The need to acquire solid estimates from the data led to the introduction of effective approaches such as the \emph{epidemiological Renormalization Group} (eRG). A recognized relevant factor impacting the evolution of pandemics is the feedback stemming from individuals' choices. The latter can be taken into account via the \textit{information index} which accommodates the information--induced perception regarding the status of the disease and the memory of past spread. We, therefore, show how to augment the eRG by means of the information index. We first develop the {\it behavioural} version of the eRG and then test it against the US vaccination campaign for COVID-19. We find that the behavioural augmented eRG improves the description of the pandemic dynamics of the US divisions for which the epidemic peak occurs after the start of the vaccination campaign. Our results strengthen the relevance of taking into account the human behaviour component when modelling pandemic evolution. To inform public health policies, the model can be readily employed to investigate the socio-epidemiological dynamics, including vaccination campaigns, for other regions of the world.

q-bio.PE↗

arXiv2023

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.

q-bio.PE↗

arXiv2023

An SIR model with viral load-dependent transmission

The viral load is known to be a chief predictor of the risk of transmission of infectious diseases. In this work, we investigate the role of the individuals' viral load in the disease transmission by proposing a new susceptible-infectious-recovered epidemic model for the densities and mean viral loads of each compartment. To this aim, we formally derive the compartmental model from an appropriate microscopic one. Firstly, we consider a multi-agent system in which individuals are identified by the epidemiological compartment to which they belong and by their viral load. Microscopic rules describe both the switch of compartment and the evolution of the viral load. In particular, in the binary interactions between susceptible and infectious individuals, the probability for the susceptible individual to get infected depends on the viral load of the infectious individual. Then, we implement the prescribed microscopic dynamics in appropriate kinetic equations, from which the macroscopic equations for the densities and viral load momentum of the compartments are eventually derived. In the macroscopic model, the rate of disease transmission turns out to be a function of the mean viral load of the infectious population. We analytically and numerically investigate the case that the transmission rate linearly depends on the viral load, which is compared to the classical case of constant transmission rate. A qualitative analysis is performed based on stability and bifurcation theory. Finally, numerical investigations concerning the model reproduction number and the epidemic dynamics are presented.

nlin.AO↗

arXiv2021

An SIR-like kinetic model tracking individuals' viral load

Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a neglected aspect is the heterogeneity of disease transmission and progression linked to the viral load of each infectious individual. Here, we attempt to investigate the interplay between the evolution of individuals' viral load and the epidemic dynamics from a theoretical point of view. In the framework of multi-agent systems, we propose a particle stochastic model describing the infection transmission through interactions among agents and the individual physiological course of the disease. Agents have a double microscopic state: a discrete label, that denotes the epidemiological compartment to which they belong and switches in consequence of a Markovian process, and a microscopic trait, representing a normalized measure of their viral load, that changes in consequence of binary interactions or interactions with a background. Specifically, we consider Susceptible--Infected--Removed--like dynamics where infectious individuals may be isolated from the general population and the isolation rate may depend on the viral load sensitivity and frequency of tests. We derive kinetic evolution equations for the distribution functions of the viral load of the individuals in each compartment, whence, via suitable upscaling procedures, we obtain a macroscopic model for the densities and viral load momentum. We perform then a qualitative analysis of the ensuing macroscopic model, and we present numerical tests in the case of both constant and viral load-dependent isolation control. Also, the matching between the aggregate trends obtained from the macroscopic descriptions and the original particle dynamics simulated by a Monte Carlo approach is investigated.

physics.soc-ph↗

arXiv2021

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

In this paper we introduce a compartmental epidemic model describing the transmission of the COVID-19 disease in presence of non-mandatory vaccination. The model takes into account the hesitancy and refusal of vaccination. To this aim, we employ the information index, which mimics the idea that individuals take their decision on vaccination based not only on the present but also on the past information about the spread of the disease. Theoretical analysis and simulations show clearly as a voluntary vaccination can certainly reduce the impact of the disease but it is unable to eliminate it. We also show how the information-related parameters affect the dynamics of the disease. In particular, the hesitancy and refusal of vaccination is better contained in case of large information coverage and small memory characteristic time. Finally, the possible influence of seasonality is also investigated.

q-bio.PE↗