Mathematical Analysis of an HIV/AIDS Model: Impact of Educational Programs and Abstinence in Sub-Saharan Africa

Competitive numerical analysis for stochastic HIV/AIDS epidemic model in a two-sex population

This study is an attempt to explain a reliable numerical analysis of a stochastic HIV/AIDS model in a two-sex population considering counselling and antiretroviral therapy (ART). The authors are comparing the solutions of the stochastic and deterministic HIV/AIDS epidemic model. Here, an endeavour has been made to explain the stochastic HIV/AIDS epidemic model is comparatively more pragmatic in contrast with the deterministic HIV/AIDS epidemic model. The effect of threshold number H^* holds on the stochastic HIV/AIDS epidemic model. If H^* < 1 then condition helps us to control disease in a two-sex human population while H^* > 1 explains the persistence of disease in the two-sex human population. Lamentably, numerical methods such as Euler-Maruyama, stochastic Euler, and stochastic Runge-Kutta do not work for large time step sizes. The recommended structure preserving framework of the stochastic non-standard finite difference (SNSFD) scheme conserve all vital characteristics such as positivity, boundedness, and dynamical consistency defined by Mickens. The effectiveness of counselling and ART may control HIV/AIDS in a two-sex population.

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.

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.

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.

Modelling effects of public health educational campaigns on drinking dynamics

This paper deals with the global property of a drinking model with public health educational campaigns. With the help of Lyapunov function, global stability of equilibria of the model is derived. The alcohol-free equilibrium is globally asymptotically stable and the alcohol problems are eliminated from population if [Formula: see text]. A unique alcohol present equilibrium is globally asymptotically stable if [Formula: see text]. Furthermore, the basic reproductive [Formula: see text] for the model is compared with the basic reproductive number [Formula: see text] for the absence of public health educational campaigns. We conclude that the public health educational campaigns of drinking individuals can slow down the drinking dynamics. Some numerical simulations are also given to explain our conclusions.

Analysis of a sex-structured HIV/AIDS model with the effect of screening of infectives

This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are determined, local stability and global stability of both the "Disease-Free Equilibrium" (DFE) and "Endemic Equilibrium" (EE) are discussed in detail. The DFE is shown to be locally and globally stable when the basic reproductive number ℛ0 is less than unity. We also prove that the EE is locally and globally asymptotically stable under some conditions. Finally, numerical simulations are reported to support the analytical findings.

The impact of the wavelet propagation distribution on SEIRS modeling with delay

Previous models of disease spread involving delay have used basic SIR (susceptible--infectious--recovery) formulae and approaches. This paper demonstrates how time-varying SEIRS (S--exposed--I - R - S) models can be extended with delay to produce wave propagations that simulate periodic wave fronts of disease spread in the context of population movements. The model also takes into account the natural mortality associated with the disease spread. Understanding the delay of an infectious disease is critical when attempting to predict where and how fast the disease will propagate. We use cellular automata to model the delay and its effect on the spread of infectious diseases where population movement occurs. We illustrate an approach using wavelet transform analysis to understand the impact of the delay on the spread of infectious diseases. The results indicate that including delay provides novel ways to understand the effects of migration and population movement on disease spread.

The role of screening and treatment in the transmission dynamics of HIV/AIDS and tuberculosis co-infection: a mathematical study

In this paper, we present a deterministic non-linear mathematical model for the transmission dynamics of HIV and TB co-infection and analyze it in the presence of screening and treatment. The equilibria of the model are computed and stability of these equilibria is discussed. The basic reproduction numbers corresponding to both HIV and TB are found and we show that the disease-free equilibrium is stable only when the basic reproduction numbers for both the diseases are less than one. When both the reproduction numbers are greater than one, the co-infection equilibrium point may exist. The co-infection equilibrium is found to be locally stable whenever it exists. The TB-only and HIV-only equilibria are locally asymptotically stable under some restriction on parameters. We present numerical simulation results to support the analytical findings. We observe that screening with proper counseling of HIV infectives results in a significant reduction of the number of individuals progressing to HIV. Additionally, the screening of TB reduces the infection prevalence of TB disease. The results reported in this paper clearly indicate that proper screening and counseling can check the spread of HIV and TB diseases and effective control strategies can be formulated around 'screening with proper counseling'.

Modelling the impact of HIV on the populations of South Africa and Botswana

We develop and use mathematical models that describe changes in the South African population over the last decades, brought on by HIV and AIDS. We do not model all the phases in HIV progression but rather, we show that a relatively simple model is sufficient to represent the data and allows us to investigate important aspects of HIV infection: firstly, we are able to investigate the effect of awareness on the prevalence of HIV and secondly, it enables us to make a comparison between South Africa and Botswana. A comparison is made between two models: a model that does not reflect awareness of the devastating impact of HIV and AIDS, and a model with an added psychological awareness factor. Both models are fitted to data that reflects the incidence of HIV and AIDS within South Africa. This allows us to examine the impact of psychological awareness. We show that inclusion of the effect of awareness is absolutely necessary to arrive at a model description that satisfactorily fits the available HIV and AIDS data for South Africa. We also show that a relatively simple modelling of awareness (as opposed to more complex mathematical techniques that have been used in past studies) is sufficient to accurately describe the observed patterns in the data. Even though awareness alone is not sufficient to eradicate any disease and other control strategies should be explored and implemented concurrently with educational campaigns, we are able to conclude (through thorough model analyses procedures) that the current level of awareness in South Africa is far below the level that is effectively required to eradicate HIV from the South African population. The awareness model is also fitted to HIV-related data for Botswana and we compare the results with the South African case. Though the effect of awareness is currently estimated at a much higher level in Botswana, other factors such as poorer health care and cultural differences may play a role in limiting the ability of awareness to combat HIV in Botswana.

A MODEL FOR CONTROL OF HIV/AIDS WITH PARENTAL CARE

In this study we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyze a mathematical model that describes the dynamics of HIV infection among the immigrant youths and how parental care can minimize or prevent the spread of the disease in the population. We analyze the model with both screening control and parental care, then investigate its stability and sensitivity behavior. We also conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is globally asymptotically stable. We establish optimal strategies for the control of the disease with screening and parental care, and provide numerical simulations to illustrate the analytic results.