Optimal public health intervention in a behavioural vaccination model: the interplay between seasonality, behaviour and latency period

A game theoretic complex network model to estimate the epidemic threshold under individual vaccination behaviour and adaptive social connections

In today's interconnected world, the spread of information is closely linked to infectious disease dynamics. Public awareness plays a crucial role, as individual vaccination decisions significantly impact collective efforts to combat emerging health threats. This study explores disease transmission within a framework integrating social connections, information sharing, and individual vaccination decisions. We introduce a behaviour-prevalence model on an adaptive multiplex network, where the physical layer (Layer-II) captures disease transmission under vaccination. In contrast, the virtual layer (Layer-I) represents adaptive social contacts and the flow of information, shaping vaccination decisions within a socially influenced environment. We derive analytical expressions for the epidemic threshold using the microscopic Markov Chain Method (MMCM). Simulation results highlight that adaptive social contacts lead to a higher epidemic threshold than non-adaptive networks. Additionally, network characteristics, such as the power-law exponent in scale-free networks, significantly impact infection spread within populations. Our results reveal that changes in perceived infection risk and an individual's sensitivity to non-vaccinated neighbour's status strongly influence vaccine uptake across populations. These insights can guide public health officials in developing targeted vaccination programs that address the evolving dynamics of social connections, information dissemination, and vaccination choice in the digital era.

Vaccination games and imitation dynamics with memory

In this paper, we model dynamics of pediatric vaccination as an imitation game, in which the rate of switching of vaccination strategies is proportional to perceived payoff gain that consists of the difference between perceived risk of infection and perceived risk of vaccine side effects. To account for the fact that vaccine side effects may affect people's perceptions of vaccine safety for some period of time, we use a delay distribution to represent how memory of past side effects influences current perception of risk. We find disease-free, pure vaccinator, and endemic equilibria and obtain conditions for their stability in terms of system parameters and characteristics of a delay distribution. Numerical bifurcation analysis illustrates how stability of the endemic steady state varies with the imitation rate and the mean time delay, and this shows that it is not just the mean duration of memory of past side effects, but also the actual distribution that determines whether disease will be maintained in the population at some steady level, or if sustained periodic oscillations around this steady state will be observed. Numerical simulations illustrate a comparison of the dynamics for different mean delays and different distributions, and they show that even when periodic solutions are observed, there are differences in their amplitude and period for different distributions. We also investigate the effect of constant public health information campaigns on vaccination dynamics. The analysis suggests that the introduction of such campaigns acts as a stabilizing factor for endemic equilibrium, allowing it to remain stable for larger values of mean time delays.

Infectious Disease Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect

We propose a framework for the description of the effects of vaccinations on the spreading of an epidemic disease. Different vaccines can be dosed, each providing different immunization times and immunization levels. Differences due to individuals' ages are accounted for through the introduction of either a continuous age structure or a discrete set of age classes. Extensions to gender differences or to distinguish fragile individuals can also be considered. Within this setting, vaccination strategies can be simulated, tested and compared, as is explicitly described through numerical integrations.

How best can finite-time social distancing reduce epidemic final size?

Given maximal social distancing duration and intensity, how can one minimize the epidemic final size, or equivalently the total number of individuals infected during the outbreak? A complete answer to this question is provided and demonstrated here for the SIR epidemic model. In this simplified setting, the optimal solution consists in enforcing the highest confinement level during the longest allowed period, beginning at a time instant that is the unique solution to certain 1D optimization problem. Based on this result, we present numerical essays showing the best possible performance for a large set of basic reproduction numbers and lockdown durations and intensities.

Optimal Immunity Control and Final Size Minimization by Social Distancing for the SIR Epidemic Model

The aim of this article is to understand how to apply partial or total containment to SIR epidemic model during a given finite time interval in order to minimize the epidemic final size, that is the cumulative number of cases infected during the complete course of an epidemic. The existence and uniqueness of an optimal strategy are proved for this infinite-horizon problem, and a full characterization of the solution is provided. The best policy consists in applying the maximal allowed social distancing effort until the end of the interval, starting at a date that is not always the closest date and may be found by a simple algorithm. Both theoretical results and numerical simulations demonstrate that it leads to a significant decrease in the epidemic final size. We show that in any case the optimal intervention has to begin before the number of susceptible cases has crossed the herd immunity level, and that its limit is always smaller than this threshold. This problem is also shown to be equivalent to the minimum containment time necessary to stop at a given distance after this threshold value.