Oscillation thresholds via the novel MBR method with application to oncolytic virotherapy

Oncolytic virotherapy is a therapy for the treatment of malignant tumours. In some undesirable cases, the injection of viral particles can lead to stationary oscillations, thus preventing the full destruction of the tumour mass. We investigate the oscillation thresholds in a model for the dynamics of a tumour under treatment with an oncolytic virus. To this aim, we employ the minimum bifurcation roots (MBR) method, which is a novel approach to determine the existence and location of Hopf bifurcations. The application to oncolytic virotherapy confirms how this approach may be more manageable than classical methods based on the Routh–Hurwitz criterion. In particular, the MBR method allows to explicitly identify a range of values in which the oscillation thresholds fall

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.Comment: 18 pages, 4 figures. arXiv admin note: text overlap with arXiv:2106.1448

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

Clinical features and outcomes of elderly hospitalised patients with chronic obstructive pulmonary disease, heart failure or both

Background and objective: Chronic obstructive pulmonary disease (COPD) and heart failure (HF) mutually increase the risk of being present in the same patient, especially if older. Whether or not this coexistence may be associated with a worse prognosis is debated. Therefore, employing data derived from the REPOSI register, we evaluated the clinical features and outcomes in a population of elderly patients admitted to internal medicine wards and having COPD, HF or COPD + HF. Methods: We measured socio-demographic and anthropometric characteristics, severity and prevalence of comorbidities, clinical and laboratory features during hospitalization, mood disorders, functional independence, drug prescriptions and discharge destination. The primary study outcome was the risk of death. Results: We considered 2,343 elderly hospitalized patients (median age 81 years), of whom 1,154 (49%) had COPD, 813 (35%) HF, and 376 (16%) COPD + HF. Patients with COPD + HF had different characteristics than those with COPD or HF, such as a higher prevalence of previous hospitalizations, comorbidities (especially chronic kidney disease), higher respiratory rate at admission and number of prescribed drugs. Patients with COPD + HF (hazard ratio HR 1.74, 95% confidence intervals CI 1.16-2.61) and patients with dementia (HR 1.75, 95% CI 1.06-2.90) had a higher risk of death at one year. The Kaplan-Meier curves showed a higher mortality risk in the group of patients with COPD + HF for all causes (p = 0.010), respiratory causes (p = 0.006), cardiovascular causes (p = 0.046) and respiratory plus cardiovascular causes (p = 0.009). Conclusion: In this real-life cohort of hospitalized elderly patients, the coexistence of COPD and HF significantly worsened prognosis at one year. This finding may help to better define the care needs of this population

Problemi di controllo in epidemiologia matematica e comportamentale

Nonostante i progressi nell'eliminazione di infezioni da lungo in circolazione, gli ultimi decenni hanno visto la continua comparsa o ricomparsa di malattie infettive. Esse non solo minacciano la salute globale, ma i costi generati da epidemie nell\u2019uomo e negli animali sono responsabili di significative perdite economiche. I modelli matematici della diffusione di malattie infettive hanno svolto un ruolo significativo nel controllo delle infezioni. Da un lato, hanno dato un importante contributo alla comprensione epidemiologica degli andamenti di scoppi epidemici; d'altro canto, hanno concorso a determinare come e quando applicare le misure di controllo al fine di contenere rapidamente ed efficacemente le epidemie. Ciononostante, per dare forma alle politiche di sanit\ue0 pubblica, \ue8 essenziale acquisire una migliore e pi\uf9 completa comprensione delle azioni efficaci per controllare le infezioni, impiegando nuovi livelli di complessit\ue0. Questo \ue8 stato l'obiettivo fondamentale della ricerca che ho svolto durante il dottorato; in questa tesi i prodotti di questa ricerca sono raccolti e interconnessi. Tuttavia, poich\ue9 fuori contesto, altri problemi a cui mi sono interessata sono stati esclusi: essi riguardano le malattie autoimmuni e l'ecologia del paesaggio. Si inizia con un capitolo introduttivo, che ripercorre la storia dei modelli epidemici, le motivazioni e gli incredibili progressi. Sono due gli aspetti su cui ci concentriamo: i) la valutazione qualitativa e quantitativa di strategie di controllo specifiche per il problema in questione (attraverso, ad esempio, il controllo ottimo o le politiche a soglia); ii) l'incorporazione nel modello dei cambiamenti nel comportamento umano in risposta alla dinamica della malattia. In questo quadro si inseriscono e contestualizzano i nostri studi. Di seguito, a ciascuno di essi \ue8 dedicato un capitolo specifico. Le tecniche utilizzate includono la costruzione di modelli appropriati dati da equazioni differenziali ordinarie non lineari, la loro analisi qualitativa (tramite, ad esempio, la teoria della stabilit\ue0 e delle biforcazioni), la parametrizzazione e la validazione con i dati disponibili. I test numerici sono eseguiti con avanzati metodi di simulazione di sistemi dinamici. Per i problemi di controllo ottimo, la formulazione segue l'approccio classico di Pontryagin, mentre la risoluzione numerica \ue8 svolta da metodi di ottimizzazione sia diretta che indiretta. Nel capitolo 1, utilizzando come base di partenza un modello Suscettibili-Infetti-Rimossi, affrontiamo il problema di minimizzare al contempo la portata e il tempo di eradicazione di un\u2019epidemia tramite strategie di vaccinazione o isolamento ottimali. Un modello epidemico tra due sottopopolazioni, che descrive la dinamica di Suscettibili e Infetti in malattie della fauna selvatica, \ue8 formulato e analizzato nel capitolo 2. Qui, vengono confrontati due tipi di strategie di abbattimento localizzato: proattivo e reattivo. Il capitolo 3 tratta di un modello per la trasmissione di malattie pediatriche prevenibili con vaccino, dove la vaccinazione dei neonati segue la dinamica del gioco dell\u2019imitazione ed \ue8 affetta da campagne di sensibilizzazione da parte del sistema sanitario. La vaccinazione \ue8 anche incorporata nel modello del capitolo 4. Qui, essa \ue8 rivolta a individui suscettibili di ogni et\ue0 ed \ue8 funzione dell\u2019informazione e delle voci circolanti sulla malattia. Inoltre, si assume che l'efficacia del vaccino sia parziale ed evanescente col passare del tempo. L'ultimo capitolo \ue8 dedicato alla tuttora in corso pandemia di COVID-19. Si costruisce un modello epidemico con tassi di contatto e di quarantena dipendenti dall\u2019informazione circolante. Il modello \ue8 applicato al caso italiano e incorpora le progressive restrizioni durante il lockdown.Despite major achievements in eliminating long-established infections (as in the very well known case of smallpox), recent decades have seen the continual emergence or re-emergence of infectious diseases (last but not least COVID-19). They are not only threats to global health, but direct and indirect costs generated by human and animal epidemics are responsible for significant economic losses worldwide. Mathematical models of infectious diseases spreading have played a significant role in infection control. On the one hand, they have given an important contribution to the biological and epidemiological understanding of disease outbreak patterns; on the other hand, they have helped to determine how and when to apply control measures in order to quickly and most effectively contain epidemics. Nonetheless, in order to shape local and global public health policies, it is essential to gain a better and more comprehensive understanding of effective actions to control diseases, by finding ways to employ new complexity layers. This was the main focus of the research I have carried out during my PhD; the products of this research are collected and connected in this thesis. However, because out of context, other problems I interested in have been excluded from this collection: they rely in the fields of autoimmune diseases and landscape ecology. We start with an Introduction chapter, which traces the history of epidemiological models, the rationales and the breathtaking incremental advances. We focus on two critical aspects: i) the qualitative and quantitative assessment of control strategies specific to the problem at hand (via e.g. optimal control or threshold policies); ii) the incorporation into the model of the human behavioral changes in response to disease dynamics. In this framework, our studies are inserted and contextualized. Hereafter, to each of them a specific chapter is devoted. The techniques used include the construction of appropriate models given by non-linear ordinary differential equations, their qualitative analysis (via e.g. stability and bifurcation theory), the parameterization and validation with available data. Numerical tests are performed with advanced simulation methods of dynamical systems. As far as optimal control problems are concerned, the formulation follows the classical approach by Pontryagin, while both direct and indirect optimization methods are adopted for the numerical resolution. In Chapter 1, within a basic Susceptible-Infected-Removed model framework, we address the problem of minimizing simultaneously the epidemic size and the eradication time via optimal vaccination or isolation strategies. A two-patches metapopulation epidemic model, describing the dynamics of Susceptibles and Infected in wildlife diseases, is formulated and analyzed in Chapter 2. Here, two types of localized culling strategies are considered and compared: proactive and reactive. Chapter 3 concerns a model for vaccine-preventable childhood diseases transmission, where newborns vaccination follows an imitation game dynamics and is affected by awareness campaigns by the public health system. Vaccination is also incorporated in the model of Chapter 4. Here, it addresses susceptible individuals of any age and depends on the information and rumors about the disease. Further, the vaccine effectiveness is assumed to be partial and waning over time. The last Chapter 5 is devoted to the ongoing pandemic of COVID-19. We build an epidemic model with information-dependent contact and quarantine rates. The model is applied to the Italian case and explicitly incorporates the progressive lockdown restrictions

Effects of information-induced behavioural changes during the COVID-19 lockdowns: the case of Italy

The COVID-19 pandemic that started in China in December 2019 has not only threatened world public health, but severely impacted almost every facet of life, including behavioural and psychological aspects. In this paper, we focus on the 'human element' and propose a mathematical model to investigate the effects on the COVID-19 epidemic of social behavioural changes in response to lockdowns. We consider an SEIR-like epidemic model where the contact and quarantine rates depend on the available information and rumours about the disease status in the community. The model is applied to the case of the COVID-19 epidemic in Italy. We consider the period that stretches between 24 February 2020, when the first bulletin by the Italian Civil Protection was reported and 18 May 2020, when the lockdown restrictions were mostly removed. The role played by the information-related parameters is determined by evaluating how they affect suitable outbreak-severity indicators. We estimate that citizen compliance with mitigation measures played a decisive role in curbing the epidemic curve by preventing a duplication of deaths and about 46% more infections

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.Comment: 20 pages, 5 figure

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