Objective-An extensive literature uses reconstructed historical smoking rates by birth-cohort to inform anti-smoking policies. This paper examines whether and how these rates change when one adjusts for differential mortality of smokers and non-smokers. Dynamics, 1986Dynamics, , 1999Dynamics, , 2001Dynamics, , 2003Dynamics, , 2005, the UK (British Household Panel Survey, 1999, 2002, and Russia (Russian Longitudinal Monitoring Study, 2000), we generate life-course smoking prevalence rates by age-cohort. With cause-specific death rates from secondary sources and an improved method, we correct for differential mortality, and we test whether adjusted and unadjusted rates statistically differ. With US data (National Health Interview Survey, 1967-2004, we also compare contemporaneously measured smoking prevalence rates with the equivalent rates from retrospective data. Methods-Using retrospectively reported data from the US (Panel Study of IncomeResults-We find that differential mortality matters only for men. For Russian men over age 70 and US and UK men over age 80 unadjusted smoking prevalence understates the true prevalence. Results using retrospective and contemporaneous data are similar.Conclusions-Differential mortality bias affects our understanding of smoking habits of old cohorts and, therefore, of inter-generational patterns of smoking. Unless one focuses on the young, policy recommendations based on unadjusted smoking rates may be misleading.
In this paper, we present an intensive investigation of the finite volume method (FVM) compared to the finite difference methods (FDMs). In order to show the main difference in the way of approaching the solution, we take the Burgers equation and the Buckley–Leverett equation as examples to simulate the previously mentioned methods. On the one hand, we simulate the results of the finite difference methods using the schemes of Lax–Friedrichs and Lax–Wendroff. On the other hand, we apply Godunov’s scheme to simulate the results of the finite volume method. Moreover, we show how starting with a variational formulation of the problem, the finite element technique provides piecewise formulations of functions defined by a collection of grid data points, while the finite difference technique begins with a differential formulation of the problem and continues to discretize the derivatives. Finally, some graphical and numerical comparisons are provided to illustrate and corroborate the differences between these two main methods.
We propose in this paper a prophylactic treatment strategy for a predator-prey system. The objective is to fight against the propagation of an infectious disease within two populations, one of which preys on the other. This propagation is modeled by means of an SIS (susceptible-infectious-susceptible) epidemic model with vital dynamics and infection propagation in both species through contact and predation, including mortality rates in both populations due directly to the disease. Treatment strategies are represented by new parameters modeling the uptake rates in the populations. We analyze the effect of various treatment strategy scenarios (prey only, predator only, or both) via their uptake rates and possible cost structures, on the size of the infected populations. We illustrate if and when applying such preventive treatments lead to a disease prevalence drop in both populations. We conduct our study using an optimal control model seeking to minimize the treatment cost(s), subject to the transmission dynamics and predator-prey dynamics.
In this paper, we study an asymmetric game that characterizes the intentions of players to adopt a vaccine. The game describes a decision-making process of two players differentiated by income level and perceived treatment cost, who consider a vaccination against an infectious disease. The process is a noncooperative game since their vaccination decision has a direct impact on vaccine coverage in the population. We introduce a replicator dynamics (RD) to investigate the players' optimal strategy selections over time. The dynamics reveal the long-term stability of the unique Nash-Pareto equilibrium strategy of this game, which is an extension of the notion of an evolutionarily stable strategy pair for asymmetric games. This Nash-Pareto pair is dependent on perceived costs to each player type, on perceived loss upon getting infected, and on the probability of getting infected from an infected person. Last but not least, we introduce a payoff parameter that plays the role of cost-incentive towards vaccination. We use an optimal control problem associated with the RD system to show that the Nash-Pareto pair can be controlled to evolve towards vaccination strategies that lead to a higher overall expected vaccine coverage.
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