On the backward bifurcation of a vaccination model with nonlinear incidence

A compartmental epidemic model, introduced by Gumel and Moghadas [1], is considered. The model incorporates a nonlinear incidence rate and an imperfect preventive vaccine given to susceptible individuals. A bifurcation analysis is performed by applying the bifurcation method introduced in [2], which is based on the use of the center manifold theory. Conditions ensuring the occurrence of backward bifurcation are derived. The obtained results are numerically validated and then discussed from both the mathematical and the epidemiological perspective

Study of RPC gas mixtures for the ARGO-YBJ experiment

The ARGO-YBJ experiment consists of a RPC carpet to be operated at the Yangbajing laboratory (Tibet, P.R. China), 4300 m a.s.l., and devoted to the detection of showers initiated by photon primaries in the energy range 100 GeV - 20 TeV. The measurement technique, namely the timing on the shower front with a few tens of particles, requires RPC operation with 1 ns time resolution, low strip multiplicity, high efficiency and low single counting rate. We have tested RPCs with many gas mixtures, at sea level, in order to optimize these parameters. The results of this study are reported.Comment: 6 pages, 3 figures. To be published in Nucl. Instr. Meth. A, talk given at the "5th International Workshop on RPCs and Related Detectors", Bari (Italy) 199

Seasonality in epidemic models: a literature review

We provide a review of some key literature results on the influence of seasonality and other time heterogeneities of contact rates, and other parameters, such as vaccination rates, on the spread of infectious diseases. This is a classical topic where highly theoretical methodologies have provided new insight on the seemingly random behavior observed in epidemic time-series. We follow the line of providing a highly personal non-systematic review of this topic, mainly based on the history of mathematical epidemiology and on the impact of reviewed articles. Our aim is to stress some issues of increasing interest, such as the public health implications of the biomathematical literature and the impact of seasonality on epidemic extinction or elimination

Time heterogeneous programs of vaccination awareness: modeling and analysis

We investigate the role of time heterogeneity of public health systems efforts in favoring the propensity of parents to vaccinate their newborns against a target childhood disease. The starting point of our investigation is the behavioral-epidemiology model proposed by d’Onofrio et al. (PLoS ONE 7:e45653, 2012), where the PHS effort was assumed to be constant. We also consider the co-presence of another layer of temporal heterogeneity: seasonality in the contact rate of the disease. We mainly assume that the effort is periodic with a 1-year period because of alternating working and holiday periods. We show that if the average effort is larger than a threshold, then the disease can be eliminated leading to an ideal equilibrium point with 100% of vaccinated newborns. A more realistic disease-free equilibrium can also be reached, under a condition that depends on the whole form of the time profile describing the PHS effort. We also generalize our disease elimination-related results to a wide class of time-heterogenous PHS efforts. Finally, we analytically show that if the disease elimination is not reached, then the disease remains uniformly persistent

Preface to the special issue on “Demographic and temporal heterogeneities in infectious disease epidemiology

No Abstrac

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

Mathematical modeling of oxygen control in biocell composting plants

We propose an optimal control problem to determine the best aeration strategy for aerobic biodegradation in a composting cell. The goal is to minimize the deviation of the oxygen level from its reference value for the entire duration of the biodegradation process. The mathematical model includes several chemical phenomena, like the aerobic biodegradation of the soluble substrate by means of a bacterial biomass, the hydrolysis of insoluble substrate and the biomass decay. The oxygen and the optimal mechanical aeration time profiles are obtained and discussed. Finally, the plant performance is evaluated in absence and presence of external aeration by means of several specific indices

A minimum time control problem for aerobic degradation processes in biocell composting plants

We introduce a mathematical model for the composting process in biocells. The model includes several phenomena, like the aerobic biodegradation of the soluble substrate by means of a bacterial population, the hydrolysis of insoluble substrate, and the biomass decay. We investigate the best strategies to reduce substrate components in minimal time by controlling the effects of cell oxygen concentration on the degradation phenomenon. It is shown that singular controls are not optimal for this model and the optimal control time profiles are of bang or bang-bang type. The occurrence of switching curves is discussed. In the case of a bang-bang control we prove that optimal control profiles have a unique switching time and the corresponding switching curve is determined