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Standard-dose quadrivalent influenza vaccines (QIV) are designed to provide protection against all four influenza strains. Adjuvanted QIV (aQIV), indicated for individuals aged 65+ years, combines MF59® adjuvant (an oil-in-water emulsion of squalene oil) with a standard dose of antigen, and is designed to produce stronger and longer immune response, especially in the elderly where immunosenescence reduces vaccine effectiveness. This study evaluated the cost-effectiveness of aQIV vs. egg-based standard-dose QIV (QIVe) in the elderly population, from the payer and societal perspective in Spain. A dynamic transmission model, which accounts for herd protection, was used to predict the number of medically attended infections in Spain. A decision tree structure was used to forecast influenza-related costs and benefits. Influenza-related probabilities of outpatient visit, hospitalization, work absenteeism, mortality, and associated utilities and costs were extracted from Spanish and European published literature. Relative vaccine effectiveness (rVE) was sourced from two different meta-analyses: the first meta-analysis was informed by laboratory-confirmed influenza studies only, resulting in a rVE = 34.6% (CI95% 2–66%) in favor of aQIV; the second meta-analysis included real world evidence influenza-related medical encounters outcomes, resulting in a rVE = 13.9% (CI95% 4.2–23.5%) in benefit of aQIV. All costs were expressed in 2021 euros. Results indicate that replacing QIVe with aQIV in the Spanish elderly population would prevent on average 43,664 influenza complicated cases, 1111 hospitalizations, and 569 deaths (with a rVE = 34.6%) or 19,104 influenza complicated cases, 486 hospitalizations, and 252 deaths (with a rVE = 13.9%). When the rVE of aQIV vs. QIVe is 34.6%, the incremental cost per quality adjusted life years (QALY) gained was €2240 from the payer; from the societal perspective, aQIV was cost saving compared with QIVe. If the rVE was 13.9%, the incremental cost per QALY was €6694 and €3936 from the payer and societal perspective, respectively. Sensitivity analyses validated the robustness of these findings. Results indicate that replacing QIVe with aQIV in the Spanish elderly population is a cost-effective strategy for the Spanish healthcare system.

In this survey, we propose an overview on Lyapunov functions for a variety of compartmental models in epidemiology. We exhibit the most widely employed functions, and provide a commentary on their use. Our aim is to provide a comprehensive starting point to readers who are attempting to prove global stability of systems of ODEs. The focus is on mathematical epidemiology, however some of the functions and strategies presented in this paper can be adapted to a wider variety of models, such as prey–predator or rumor spreading.

In this paper, we analyze some epidemic models by considering a time-varying transmission rate in complex heterogeneous networks. The transmission rate is assumed to change in time, due to a switching signal, and since the spreading of the disease also depends on connections between individuals, the population is modeled as a heterogeneous network. We establish some stability results related to the behavior of the time-weighted average Basic Reproduction Number (BRN). Later, a Susceptible–Exposed–Infectious–Recovered (SEIR) model which describes the measles disease is proposed and we show that its dynamics is determined by a threshold value, below which the disease dies out. Moreover, compared with models without the Exposed compartment, we can find weaker stability results. A control strategy with an imperfect vaccine is applied, to determine how it could effect the size of the peak. Due to the periodic behavior of the switching rule, we compare the results with the BRN of the model. Some simulations are given, using a scale-free network, to illustrate the threshold conditions found.

With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic considerations and provide a theoretical result on the probability of the extinction of the disease. Based on this calibration, we explore the variability in disease spread by stochastic simulations. In particular, we demonstrate how important epidemic indices change as a function of the contagiousness of the disease and the connectivity of the network. Our results quantify the role of starting node degree in determining these indices, commonly used to describe epidemic spread.

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We study a multi‐group SAIRS‐type epidemic model with vaccination. The role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission pattern of the disease among the groups in which the population is divided. This is a natural extension of the homogeneous mixing SAIRS model with vaccination studied in Ottaviano et. al (2021) to a network of communities. We provide a global stability analysis for the model. We determine the value of the basic reproduction number and prove that the disease‐free equilibrium is globally asymptotically stable if . In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease‐free equilibrium also when . Moreover, if , the disease‐free equilibrium is unstable and a unique endemic equilibrium exists. First, we investigate the local asymptotic stability of the endemic equilibrium and subsequently its global stability, for two variations of the original model. Last, we provide numerical simulations to compare the epidemic spreading on different networks topologies.

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