Vaccination Strategies against Seasonal Influenza in Long Term Care Setting: Lessons from a Mathematical Modelling Study.

BACKGROUND: seasonal influenza in nursing homes is a major public health concern, since in EU 43,000 long term care (LTC) facilities host an estimated 2.9 million elderly residents. Despite specific vaccination campaigns, many outbreaks in such institutions are occasionally reported. We explored the dynamics of seasonal influenza starting from real data collected from a nursing home located in Italy and a mathematical model. Our aim was to identify the best vaccination strategy to minimize cases (and subsequent complications) among the guests. MATERIALS AND METHODS: after producing the contact matrices with surveys of both the health care workers (HCW) and the guests, we developed a mathematical model of the disease. The model consists of a classical SEIR part describing the spreading of the influenza in the general population and a stochastic agent based model that formalizes the dynamics of the disease inside the institution. After a model fit of a baseline scenario, we explored the impact of varying the HCW and guests parameters (vaccine uptake and vaccine efficacy) on the guest attack rates (AR) of the nursing home. RESULTS: the aggregate AR of influenza like illness in the nursing home was 36.4% (ward1 = 56%, ward2 = 33.3%, ward3 = 31.7%, ward4 = 34.5%). The model fit to data returned a probability of infection of the causal contact of 0.3 and of the shift change contact of 0.2. We noticed no decreasing or increasing AR trend when varying the HCW vaccine uptake and efficacy parameters, whereas the increase in both guests vaccine efficacy and uptake parameter was accompanied by a slight decrease in AR of all the wards of the LTC facility. CONCLUSION: from our findings we can conclude that a nursing home is still an environment at high risk of influenza transmission but the shift change room and the handover situation carry no higher relative risk. Therefore, additional preventive measures in this circumstance may be unnecessary. In a closed environment such as a LTC facility, the vaccination of guests, rather than HCWs, may still represent the cornerstone of an effective preventive strategy. Finally, we think that the extensive inclusion of real life data into mathematical models is promising and may represent a starting point for further applications of this methodology.

Optimal vaccination choice, vaccination games, and rational exemption: an appraisal.

A threat for vaccination policies might be the onset of "rational" exemption, i.e. the family's decision not to vaccinate children after a seemingly rational comparison between the perceived risk of infection and the perceived risk of vaccine side effects. We study the implications of rational exemption by models of vaccination choice. By a simple model of individual choice we first prove the "elimination impossible" result in presence of informed families, i.e. aware of herd immunity, and suggest that limited information might explain patterns of universal vaccination. Next, we investigate vaccination choice in a game-theoretic framework for communities stratified into two groups, "pro" and "anti" vaccinators, having widely different perceived costs of infection and of vaccine side effects. We show that under informed families neither a Nash nor a Stackelberg behaviour (characterized, respectively, by players acting simultaneously and by an asymmetric situation with a "leader" and a "follower) allow elimination, unless "pro-vaccinators" assign no costs to vaccine side effects. Elimination turns out to be possible when cooperation is encouraged by a social planner, provided, however, he incorporates in the "social loss function" the preferences of anti-vaccinators only. This allows an interpretation of the current Italian vaccination policy.

Fatal SIR diseases and rational exemption to vaccination.

A challenge to disease control in modern societies is the spread of rational exemption to vaccination as a consequence of the rational comparison between the steadily declining risk of infection and the risk of side effects from the vaccine. Here, we consider rational exemption in an susceptible-infectious-removed (SIR) model with information-dependent vaccination where individuals use information on the disease's mortality as their information set. Using suitable assumptions on the dynamics of the population, we show the dynamic implications of the interaction between rational exemption, current and delayed information and the risk of death by the disease. In particular, we illustrate the onset of the long cycles caused by rational exemption when vaccination decisions are based on delayed informations.

Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases.

The increasing level of disease control by vaccination jointly with the growing standard of living and health of modern societies could favour the spread of exemption as a "rational" behaviour towards vaccination. Rational exemption implies that families will tend to relate the decision to vaccinate their children to the available information on the state of the disease. Using an SIR model with information dependent vaccination we show that rational exemption might make elimination of the disease an unfeasible task even if coverages as high as 100% are actually reached during epochs of high social alarm. Moreover, we show that rational exemption may also become responsible for the onset of sustained oscillations when the decision to vaccinate also depends on the past history of the disease.

Population-induced oscillations in blended SI-SEI epidemiological models.

The effects of standard patterns of population growth in blended SI-SEI models (of which models for 'fast and slow' tuberculosis are an instance) are considered. When the incidence has the 'true mass action' form, the system is globally stable under both exponential and logistic population dynamics, whereas sustained oscillations occur in the case of bilinear incidence. This shows in the final analysis, the minimal dynamical ingredients needed to generate oscillations in basic epidemiological models: provided the population is exponentially growing and the incidence is bilinear, at least a fraction of the newly exposed individuals must enter the infective state with a delay.