Optimal control of HIV/AIDS in the workplace in the presence of careless individuals

Exploring the seasonality and optimal control strategy of HIV/AIDS epidemic in China: The impact of seasonal testing

In this work, we investigate how the seasonal variation in the number of individuals who are tested for an HIV antibody in outpatient clinics affects the HIV transmission patterns in China, which has not been well studied. Based on the characteristics of outpatient testing data and reported cases, we establish a periodic infectious disease model to study the impact of seasonal testing on HIV transmission. The results indicate that the seasonal testing is a driving factor for the seasonality of new cases. We demonstrate the feasibility of ending the HIV/AIDS epidemic. We find that the diagnostic rates related to testing play a crucial role in controlling the size of the epidemic. Specifically, when considering minimizing both infected individuals and diagnostic rates, the level of attention paid to undiagnosed infected individuals is always positively correlated with the optimal diagnostic rates, while the optimal diagnostic rates are negatively correlated with the size of the epidemic at the terminal time.

A holistic exploration of the optimal control strategies on an enhanced mathematical model for the co-infection of HIV/AIDS and varicella-zoster

Because of its high contagiousness and correlation with HIV/AIDS complaints, the virus that causes varicella-zoster virus and its interactions have major consequences for a considerable portion of people worldwide. The primary aim of this work is to suggest and examine optimal control methods for managing the transmission dynamics of HIV/AIDS and Varicella-Zoster co-infection, using an integer model approach. The mathematical analyses of the proposed integer order model places particular emphases on the boundedness and non-negativity of the model solutions, scrutinizing equilibrium points, determining the models basic reproduction ratios (the models basic reproduction numbers) through the next-generation matrix operator method, and assessing the model equilibrium points existences and stabilities in local approach by considering the local stability conditions of Routh and Hurwitz. Additionally, it incorporates an optimal control framework to enhance our understanding of the dynamics involved in the spreading of HIV/AIDS and Varicella-Zoster co-infection within a considered population. This entails determining preventative measures that can be deliberately put into place to lessen the effects of these co-infections. The solutions of the HIV/AIDS and Varicella-Zoster co-infection model converges to the co-infection endemic equilibrium point whenever the associated basic reproduction number is greater than unity, as verified by numerical simulation results. Including optimal management gives the research an innovative viewpoint and helps identify tactical ways to mitigate the negative effects of this co-infection on the public health. The results highlight how crucial it is to address these complex structures in order to protect and improve public health outcomes. Implementing the proposed protection measures and treatment measures simultaneously has most effective result to minimize and eliminate the HIV/AIDS and Varicella-Zoster co-infection disease throughout the population.

Optimal Control and Bifurcation Analysis of HIV Model

In this study, a very crucial stage of HIV extinction and invisibility stages are considered and a modified mathematical model is developed to describe the dynamics of infection. Moreover, the basic reproduction number R ₀ is computed using the next-generation matrix method whereas the stability of disease-free equilibrium is investigated using the eigenvalue matrix stability theory. Furthermore, if R ₀ ≤ 1, the disease-free equilibrium is stable both locally and globally whereas if R ₀ > 1, based on the forward bifurcation behavior, the endemic equilibrium is locally and globally asymptotically stable. Particularly, at the critical point R ₀ = 1, the model exhibits forward bifurcation behavior. On the other hand, the optimal control problem is constructed and Pontryagin's maximum principle is applied to form an optimality system. Further, forward fourth-order Runge-Kutta's method is applied to obtain the solution of state variables whereas Runge-Kutta's fourth-order backward sweep method is applied to obtain solution of adjoint variables. Finally, three control strategies are considered and a cost-effective analysis is performed to identify the better strategies for HIV transmission and progression. In advance, prevention control measure is identified to be the better strategy over treatment control if applied earlier and effectively. Additionally, MATLAB simulations were performed to describe the population's dynamic behavior.

Analysing transmission dynamics of HIV/AIDS with optimal control strategy and its controlled state

HIV is a virus that weakens a person's immune system. HIV has three stages, and AIDS is the most severe stage of HIV (Stage 3). People with HIV should take medicine (called ART) recommended by WHO as soon as possible to reduce the amount of virus in the body. In this paper, we formulate a mathematical model for HIV/AIDS with a new approach by focusing on two groups of infectious individuals, HIV and AIDS. We also introduce a controlled class (treated patients and being monitored), and people in this class can spread the disease. We further investigate the essential dynamics of the model through an equilibrium analysis. Optimal control theory is applied to explore effective treatment strategies by combining two control measures: standard antiretroviral therapy and AIDS treatments. Numerical simulation results show the effects of the two time-dependent controls, and they can be used as guidelines for public health interventions.

Mathematical Analysis of an Industrial HIV/AIDS Model that Incorporates Carefree Attitude Towards Sex

A nonlinear differential equation model is proposed to study the dynamics of HIV/AIDS and its effects on workforce productivity. The disease-free equilibrium point of the model is shown to be locally asymptotically stable when the associated basic reproduction number [Formula: see text] is less than unity. The model is also shown to exhibit multiple endemic states for some parameter values when [Formula: see text] and [Formula: see text]. Global asymptotic stability of the disease-free equilibrium is guaranteed only when the fractions of the Susceptible subclass populations are within some bounds. Optimal control analysis of the model revealed that the most cost effective strategy that should be adopted in the fight against HIV/AIDS spread within the workforce is one that seeks to prevent infections and the treatment of infected individuals.

Mathematical Model for Optimal Control of Soil-Transmitted Helminth Infection

In this paper, we study the dynamics of soil-transmitted helminth infection. We formulate and analyse a deterministic compartmental model using nonlinear differential equations. The basic reproduction number is obtained and both disease-free and endemic equilibrium points are shown to be asymptotically stable under given threshold conditions. The model may exhibit backward bifurcation for some parameter values, and the sensitivity indices of the basic reproduction number with respect to the parameters are determined. We extend the model to include control measures for eradication of the infection from the community. Pontryagian's maximum principle is used to formulate the optimal control problem using three control strategies, namely, health education through provision of educational materials, educational messages to improve the awareness of the susceptible population, and treatment by mass drug administration that target the entire population(preschool- and school-aged children) and sanitation through provision of clean water and personal hygiene. Numerical simulations were done using MATLAB and graphical results are displayed. The cost effectiveness of the control measures were done using incremental cost-effective ratio, and results reveal that the combination of health education and sanitation is the best strategy to combat the helminth infection. Therefore, in order to completely eradicate soil-transmitted helminths, we advise investment efforts on health education and sanitation controls.

Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures

Vaccination and treatment are the most effective ways of controlling the transmission of most infectious diseases. While vaccination helps susceptible individuals to build either a long-term immunity or short-term immunity, treatment reduces the number of disease-induced deaths and the number of infectious individuals in a community/nation. In this paper, a nonlinear deterministic model with time-dependent controls has been proposed to describe the dynamics of bacterial meningitis in a population. The model is shown to exhibit a unique globally asymptotically stable disease-free equilibrium ℰ₀, when the effective reproduction number ℛ_VT ≤ 1, and a globally asymptotically stable endemic equilibrium ℰ₁, when ℛ_VT > 1; and it exhibits a transcritical bifurcation at ℛ_VT = 1. Carriers have been shown (by Tornado plot) to have a higher chance of spreading the infection than those with clinical symptoms who will sometimes be bound to bed during the acute phase of the infection. In order to find the best strategy for minimizing the number of carriers and ill individuals and the cost of control implementation, an optimal control problem is set up by defining a Lagrangian function L to be minimized subject to the proposed model. Numerical simulation of the optimal problem demonstrates that the best strategy to control bacterial meningitis is to combine vaccination with other interventions (such as treatment and public health education). Additionally, this research suggests that stakeholders should press hard for the production of existing/new vaccines and antibiotics and their disbursement to areas that are most affected by bacterial meningitis, especially Sub-Saharan Africa; furthermore, individuals who live in communities where the environment is relatively warm (hot/moisture) are advised to go for vaccination against bacterial meningitis.

Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies

We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.

Global dynamics of a heroin epidemic model with age structure and nonlinear incidence

A heroin model with nonlinear incidence rate and age structure is investigated. The basic reproduction number is determined whether or not a heroin epidemic breaks out. By employing the Lyapunov functionals, the drug-free equilibrium is globally asymptotically stable if [Formula: see text]; while the drug spread equilibrium is also globally asymptotically stable if [Formula: see text]. Our results imply that improving detected rates and drawing up the efficient prevention play more important role than increasing the treatment for drug users.

Mathematical Analysis of the Effects of HIV-Malaria Co-infection on Workplace Productivity

In this paper, a nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics and effects of HIV-malaria co-infection in the workplace. Basic reproduction numbers of sub-models are derived and are shown to have LAS disease-free equilibria when their respective basic reproduction numbers are less than unity. Conditions for existence of endemic equilibria of sub-models are also derived. Unlike the HIV-only model, the malaria-only model is shown to exhibit a backward bifurcation under certain conditions. Conditions for optimal control of the co-infection are derived using the Pontryagin's maximum principle. Numerical experimentation on the resulting optimality system is performed. Using the incremental cost-effectiveness ratio, it is observed that combining preventative measures for both diseases is the best strategy for optimal control of HIV-malaria co-infection at the workplace.