Modelling effects of public health educational campaigns on drinking dynamics

A non-standard numerical scheme for an alcohol-abuse model with induced-complications

The prevalence of alcohol-related fatalities worldwide is on the ascendancy not only Ghana, but worldwide. Although the ramifications of alcohol consumption have been the subject of several studies, alcoholism remains a serious concern in public health. This study investigates the dynamics of alcoholism in a population with consumption-induced complications using a deterministic Modelling framework. Using a novel technique, we determined a threshold parameter R 0 which we call the basic alcohol-abuse initiation number which is similar to the basic reproduction number for infectious diseases. The model has two mutually-exclusive fixed points whose existence depend on whether or not the R 0 is less or greater than unity. Global asymptotic stability of the alcohol-abuse-free fixed point is shown to be associated with R 0 ≤ 1 . Further, forward bifurcation is observed to occur at R 0 = 1 , indicating the possibility of eradication of the phenomenon of alcoholism if R 0 can be kept below unity over a sufficiently long period of time. Sensitivity analysis also revealed that the probability of initiation into alcohol-abuse by moderate drinkers (β 1 ), followed by the probability of initiation into alcohol-abuse by heavy drinkers (β 2 ) are the most the parameters with the most influence on R 0 and consequently on alcohol-abuse persistence. A non-standard finite difference scheme is also developed to numerically simulate the model so as to demonstrate the findings derived from the analysis and also to observe the impact of some epidemiological factors on the dynamics of alcohol-abuse.

Optimal control of alcoholism spreading through awareness over multiplex network

This paper proposes the SISRS epidemic model to represent alcohol addiction among people. The spreading of alcohol addiction is controlled by creating awareness among the people and also by treating them to overcome it. Multiplex network is used to study the dynamics of addiction. Alcoholism spreads over the physical contact layer and follows the SISRS process whereas human awareness spreads over the virtual contact layer and follows the UAU process. Based on the Microscopic Markov Chain Approach competing dynamics of spreading of alcohol addiction and human awareness diffusion are studied. Necessary conditions for the existence of an alcohol-free population are found. An optimal control problem using a suitable cost index is formulated to reduce the alcohol addicts and the optimal control strategy using Pontryagin’s Minimum Principle is determined. Numerical results are developed to find the effect of various parameters and to analyze the effects of different control strategies. The results obtained from this model are closer to the data collected in the National Survey of Drug Use and Health (NSDUH) from 2002 to 2018.

Global threshold dynamics of an age structured alcoholism model

We consider in this research an age-structured alcoholism model. The global behavior of the model is investigated. It is proved that the system has a threshold dynamics in terms of the basic reproduction number (BRN), where we obtained that alcohol-free equilibrium (AFE) is globally asymptotically stable (GAS) in the case [Formula: see text], but for [Formula: see text] we found that the system persists and the nontrivial equilibrium (EE) is GAS. Furthermore, the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated, which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied populations. The obtained mathematical results are tested numerically next to its biological relevance.

Threshold dynamics of a multi-group SEAR alcoholism model with public health education

In this paper, we investigate the threshold dynamics of a multi-group SEAR alcoholism epidemic model with public health education. The multi-group model allows us to describe interactions both within-group and inter-group separately. We prove that the basic reproduction number [Formula: see text] plays the role of a threshold for the long-time behavior of the model. The alcohol-free equilibrium [Formula: see text] of the model is globally asymptotically stable if [Formula: see text], while the alcohol-present equilibrium [Formula: see text] exists uniquely and is globally asymptotically stable if [Formula: see text]. For the proofs of main results, we use the classical method of Lyapunov functions and apply subtle grouping technique in estimating the derivatives of Lyapunov functions guided by graph theory. Our results expand the previous results which have been obtained in single-group models. Sensitivity analysis and numerical simulations are also performed to illustrate our results.

Spatiotemporal Distributions and Dynamics of Human Infections with the A H7N9 Avian Influenza Virus

In 2013 in mainland China, a novel avian influenza virus H7N9 began to infect humans and had aroused severe fatality in the infected humans, followed by the annual outbreaks. By methods of GIS and kriging interpolation, we get the geographical distributions. We obtain the longitudinal characteristics of these outbreaks based on statistics and diagrams. After these spatiotemporal distributions, an eco-epidemiological model is established and analyzed. In this model, the general incidence functions, the factor of fully killed infected poultry, and the virus in environment are taken into account. Theoretical analysis shows that the endemic will be formed to a large extent once the H7N9 avian influenza virus exists in poultry. On the basis of dynamics, we explore the possible disease control measures by numerical simulations. Simulations indicate that measures of vaccination in poultry and stopping live poultry transactions are the primary choices for disease control in humans, and strengthened inhibition effects and environmental disinfections can effectively control the outbreak.

Bifurcation analysis of an age-structured alcoholism model

In this paper, we investigate a new alcoholism model in which alcoholics have age structure. We rewrite the model as an abstract non-densely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analyzing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state. Furthermore, by using Hopf bifurcation theorem in Liu et al. (Z. Angew. Math. Phys. 62 (2011) 191-222), we show that Hopf bifurcation occurs at the positive steady state when bifurcating parameter crosses some critical values. Finally, we perform some numerical simulations to illustrate our theoretical results and give a brief conclusion.

The analysis of a drug transmission model with family education and public health education

In this paper, we formulate a six dimensional drug transmission model to study the effect of family education and public health education. The dynamical behaviors of the model are discussed in terms of the basic reproduction number R0. By constructing Lyapunov functions, we obtain the drug-free equilibrium is globally asymptotically stable if R0≤1 and the drug addiction equilibrium is globally asymptotically stable if R0>1. Sensitivity analyses are performed to seek for effective control measures for drug spread. The analysis show that both the family and public health education can influence the spread of drug transmission. However, the combination of family and public health education is more effective to reduce the prevalence of drugs. Some numerical simulations are given to confirm the obtained theoretical results.

Stability of a binge drinking model with delay

A more realistic binge drinking model with time delay is introduced. Time delay is used to represent the time lag of the immunity against drinking in our model. For the model without the time delay, using Routh-Hurwitz criterion, we obtain that the alcohol-free equilibrium is locally asymptotically stable if [Formula: see text]. We also obtain that the unique alcohol-present equilibrium is locally asymptotically stable if [Formula: see text]. For the model with time delay, the local stability of all the equilibria is derived. Furthermore, regardless of the time delay length, using comparison theorem and iteration technique, we obtain that the alcohol-free equilibrium is globally asymptotically stable under certain conditions. Numerical simulations are also conducted to illustrate and extend our analytic results.

Modeling the role of public health education in Ebola virus disease outbreaks in Sudan

Public involvement in Ebola Virus Disease (EVD) prevention efforts is key to reducing disease outbreaks. Targeted education through practical health information to particular groups and sub-populations is crucial to controlling the disease. In this paper, we study the dynamics of Ebola virus disease in the presence of public health education with the aim of assessing the role of behavior change induced by health education to the dynamics of an outbreak. The power of behavior change is evident in two outbreaks of EVD that took place in Sudan only 3 years apart. The first occurrence was the first documented outbreak of EVD and produced a significant number of infections. The second outbreak produced far fewer cases, presumably because the population in the region learned from the first outbreak. We derive a system of ordinary differential equations to model these two contrasting behaviors. Since the population in Sudan learned from the first outbreak of EVD and changed their behavior prior to the second outbreak, we use data from these two instances of EVD to estimate parameters relevant to two contrasting behaviors. We then simulate a future outbreak of EVD in Sudan using our model that contains two susceptible populations, one being more informed about EVD. Our finding show how a more educated population results in fewer cases of EVD and highlights the importance of ongoing public health education.