1,720,965 research outputs found
Volatile opinions and optimal control of vaccine awareness campaigns: chaotic behaviour of the Forward-Backward Sweep algorithm vs heuristic direct optimization
Full text linkIn modern societies the main sources of information are Internet-based social networks. Thus, the opinion of citizens on key topics, such as vaccines, is very volatile. Here, we explore the impact of volatility on the modelling of public response to vaccine awareness campaigns for favouring vaccine uptake. We apply a quasi-steady-state approximation to the model of spread and control of Susceptible-Infected-Removed diseases proposed in (d’Onofrio et al., PLoS One, 2012). This allows us to infer and analyze a new behavioural epidemiology model that is nonlinear in the control. Then, we investigate the efficient design of vaccine awareness campaigns by adopting optimal control theory. The resulting problem has important issues: (i) the integrand of its objective functional is non-convex; (ii) the application of forward-backward sweep (FBS) and gradient descent algorithms in some key cases does not work; (iii) analytical approaches provide continuous solutions that cannot rigorously be implemented since Public Health interventions cannot be fully flexible. Thus, on the one hand, we resort to direct optimization of the objective functional via heuristic stochastic optimization, in particular via particle swarm optimization and differential evolution algorithms. On the other hand, we investigate the non-convergence of the FBS algorithm with tools of the statistical theory of nonlinear chaotic time-series. Finally, since the direct optimization algorithms are stochastic, we provide a statistical assessment of the obtained solutions
On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies
No full textMathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a major simplification consists in assuming that the infectious period is exponentially distributed, then implying that the chance of recovery is independent on the time since infection. Here, we first attempt to investigate the consequences of relaxing this assumption on the performances of time-variant disease control strategies by using optimal control theory. In the framework of a basic susceptible–infected–removed (SIR) model, an Erlang distribution of the infectious period is considered and optimal isolation strategies are searched for. The objective functional to be minimized takes into account the cost of the isolation efforts per time unit and the sanitary costs due to the incidence of the epidemic outbreak. Applying the Pontryagin’s minimum principle, we prove that the optimal control problem admits only bang–bang solutions with at most two switches. In particular, the optimal strategy could be postponing the starting intervention time with respect to the beginning of the outbreak. Finally, by means of numerical simulations, we show how the shape of the optimal solutions is affected by the different distributions of the infectious period, by the relative weight of the two cost components, and by the initial conditions
Optimal Public Health intervention in a behavioural vaccination model: the interplay between seasonality, behaviour and latency period
Full text linkHesitancy 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
A geometric analysis of the impact of large but finite switching rates on vaccination evolutionary games
Full text linkIn 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
Dynamics of a metapopulation epidemic model with localized culling
No full textA two-patches metapopulation mathematical model, describing the dynamics of Susceptibles and Infected in wildlife diseases, is presented. The two patches are identical in absence of control, and culling activities are performed in only one of them. Firstly, the dynamics of the system in absence of control is investigated. Then, two types of localized culling strategies (proactive end reactive) are considered. The proactive control is modeled by a constant culling effort, and for the ensuing model the disease free equilibrium is characterized and existence of the endemic equilibrium is discussed in terms of a suitable control reproduction number. The localized reactive control is modeled by a piecewise constant culling effort function, that introduces an extra-mortality when the number of infected individuals in the patch overcomes a given threshold. The reactive control is then analytically and numerically investigated in the frame of Filippov systems. We find that localized culling may be ineffective in controlling diseases in wild populations when the infection affects host fecundity in addition to host mortality, even leading to unexpected increases in the number of infected individuals in the nearby areas
A behavioural modelling approach to assess the impact of COVID-19 vaccine hesitancy
No full textWe introduce a compartmental epidemic model to describe the spread of COVID-19 within a population, assuming that a vaccine is available, but vaccination is not mandatory. The model takes into account vaccine hesitancy and the refusal of vaccination by individuals, which take their decision on vaccination based on both the present and past information about the spread of the disease. Theoretical analysis and simulations show that voluntary vaccination can certainly reduce the impact of the disease but is unable to eliminate it. We also demonstrate how the information-related parameters affect the dynamics of the disease. In particular, vaccine hesitancy and refusal are better contained in case of widespread information coverage and short-term memory. Finally, the possible impact of seasonality on the spread of the disease is investigated
A BEHAVIORAL CHANGE MODEL TO ASSESS VACCINATION-INDUCED RELAXATION OF SOCIAL DISTANCING DURING AN EPIDEMIC
No full textThe success of mass vaccination campaigns may be jeopardized by human risky behaviors. For example, high level of vaccination coverage may induce early relaxation of social distancing. In this paper, we focus on the mutual influence between the decline in prevalence, due to the rise in the overall immunization coverage, and the consequent decrease in the compliance to social distancing measures. We consider an epidemic model where both the vaccination rate and the disease transmission rate are influenced by human behavior, which in turn depends on the current and past information about the spread of the disease.We highlight the impact of the information-related parameters on the transient and asymptotic behavior of the system that is on the early stage of the epidemic and its final outcome. Among the main results, we evidence that sustained oscillations may be triggered by the behavioral memory in the prevalence-dependent vaccination rate. However, the relaxation of social distancing may induce a switch from a cyclic regime to damped oscillations
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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