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Information dissemination intricately intertwines with the dynamics of infectious diseases in the contemporary interconnected world. Recognizing the critical role of public awareness, individual vaccination choices appear to be an essential factor in collective efforts against emerging health threats. This study aims to characterize disease transmission dynamics under evolving social connections, information sharing, and individual vaccination decisions. To address this important problem, we present an integrated behaviour-prevalence model on an adaptive multiplex network. While the physical layer (layer-II) focuses on disease transmission under vaccination, the virtual layer (layer-I), representing individuals' social contacts, is adaptive and deals with information dissemination, resulting in the dynamics of vaccination choice in a socially influenced environment. Utilizing the microscopic Markov Chain Method (MMCM), we derive analytical expressions of the epidemic threshold for populations with different levels of perceived vaccine risk. It indicates that the adaptive nature of social contacts contributes to the higher epidemic threshold compared to non-adaptive scenarios, and numerical simulations also support that. The network topology, such as the power-law exponent of a scale-free network, also significantly influences the spreading of infections in the network population. We also observe that vaccine uptake increases proportionately with the number of individuals with a higher perceived infection risk or a higher sensitivity of an individual to their non-vaccinated neighbours. As a result, our findings provide insights for public health officials in developing vaccination programs in light of the evolution of social connections, information dissemination, and vaccination choice in the digital era.

The global impact of the COVID-19 pandemic on the livelihoods of people worldwide prompted the implementation of a range of preventive measures at local, national, and international levels. Early in the outbreak, before the vaccine became accessible, voluntary quarantine and social isolation emerged as crucial strategies to curb the spread of infection. In this research, we present a game-theoretic model to elucidate the voluntary disclosure of exposure to infected individuals within communities. By employing a fractional derivative approach to illustrate disease propagation within the compartmental model, we determine the minimum level of voluntary disclosure required to disrupt the chain of transmission and allow the epidemic to fade. Our findings suggest that higher transmission rates and increased perceived severity of infection change the externality of disclosing infected exposure, thereby contributing to a rise in the proportion of individuals opting for quarantine and reducing disease incidence. We estimate behavioral parameters and transmission rates by fitting the model to hospitalized cases in Chile, South America. Results from our paper underscore the potential for public health authorities to influence and regulate voluntary disclosure of infection during emerging outbreaks through effective risk communication, emphasizing the severity of the disease, and providing accurate information about hospital capacity to the public.

Since the recent introduction of several viable vaccines for SARS-CoV-2, vaccination uptake has become the key factor that will determine our success in containing the COVID-19 pandemic. We argue that game theory and social network models should be used to guide decisions pertaining to vaccination programmes for the best possible results. In the months following the introduction of vaccines, their availability and the human resources needed to run the vaccination programmes have been scarce in many countries. Vaccine hesitancy is also being encountered from some sections of the general public. We emphasize that decision-making under uncertainty and imperfect information, and with only conditionally optimal outcomes, is a unique forte of established game-theoretic modelling. Therefore, we can use this approach to obtain the best framework for modelling and simulating vaccination prioritization and uptake that will be readily available to inform important policy decisions for the optimal control of the COVID-19 pandemic., Comment: 15 pages, 1 figure; published in Royal Society Open Science

Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data unreliable and difficult. This paper presents a study of the Bayesian posterior distribution for unknown parameters of two chaotic discrete dynamical systems conditioned on observations of the system. The study shows how the qualitative properties of the posterior are affected by the intrinsic noise present in the data, the representation of this noise in the parameter estimation process, and the length of the data-set. The results indicate that increasing length of dataset does not significantly increase the precision of the estimate, and this is true for both periodic and chaotic data. On the other hand, increasing precision of the measurements leads to significant increase in precision of the estimated parameter in case of periodic data, but not in the case of chaotic data. These results are highly useful in designing laboratory and field-based studies in biology in general, and ecology and conservation in particular., Comment: 25 pages, 11 figures

Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination - one of the most important preventive measures of modern times - is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research., Comment: 150 pages, 42 figures; published in Physics Reports

We propose a model describing the synergetic feedback between word-of-mouth (WoM) and epidemic dynamics controlled by voluntary vaccination. We combine a game-theoretic model for the spread of WoM and a compartmental model describing $SIR$ disease dynamics in the presence of a program of voluntary vaccination. We evaluate and compare two scenarios, depending on what WoM disseminates: (1) vaccine advertising, which may occur whether or not an epidemic is ongoing and (2) epidemic status, notably disease prevalence. Understanding the synergy between the two strategies could be particularly important for organizing voluntary vaccination campaigns. We find that, in the initial phase of an epidemic, vaccination uptake is determined more by vaccine advertising than the epidemic status. As the epidemic progresses, epidemic status become increasingly important for vaccination uptake, considerably accelerating vaccination uptake toward a stable vaccination coverage., Comment: 10 pages, 2 figures

Nuclear Thermal Propulsion (NTP) is a concept which uses a nuclear reactor to heat a propellant to high temperatures without combustion and can achieve significantly greater specific impulse than chemical engines. NTP has been considered many times for human and cargo missions beyond low earth orbit. A lot of development and technical maturation of NTP components took place during the Rover/NERVA program of the 60's and early 70's. Other NTP programs and studies followed attempting to further mature the NTP concept and identify a champion customer willing to devote the funds and support the development schedule to a demonstration mission. Budgetary constraints require the use of an affordable development and qualification strategy that takes into account all the previous work performed on NTP to construct an existing database, and include lessons learned and past guidelines followed. Current guidelines and standards NASA uses for human rating chemical rocket engines is referenced. The long lead items for NTP development involve the fuel elements of the reactor and ground testing the engine system, subsystem, and components. Other considerations which greatly impact the development plans includes the National Space Policy, National Environmental Policy Act, Presidential Directive/National Security Council Memorandum #25 (Scientific or Technological Experiments with Possible Large-Scale Adverse Environmental Effects and Launch of Nuclear Systems into Space), and Safeguards and Security. Ground testing will utilize non-nuclear test capabilities to help down select components and subsystems before testing in a nuclear environment to save time and cost. Existing test facilities with minor modifications will be considered to the maximum extent practical. New facilities will be designed to meet minimum requirements. Engine and test facility requirements are based on the driving mission requirements with added factors of safety for better assurance and reliability. Emphasis will be placed on small engines, since the smaller the NTP engine, the easier it is to transport, assemble/disassemble, and filter the exhaust during tests. A new ground test concept using underground bore holes (modeled after the underground nuclear test program) to filter the NTP engine exhaust is being considered. The NTP engine system design, development, test, and evaluation plan includes many engine components and subsystems, which are very similar to those used in chemical engines, and can be developed in conjunction with them Other less mature NTP engine components and subsystems (e.g., reactor) will be thoroughly analyzed and tested to acceptable levels recommended by the referenced standards and guidelines. The affordable development strategy also considers a prototype flight test, as a final step in the development process. Preliminary development schedule estimates show that an aggressive development schedule (without much margin) will be required to be flight ready for a 2033 human mission to Mars.