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 R0 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 R0 is less or greater than unity. Global asymptotic stability of the alcohol-abuse-free fixed point is shown to be associated with R0≤1. Further, forward bifurcation is observed to occur at R0=1, indicating the possibility of eradication of the phenomenon of alcoholism if R0 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 (ß1), followed by the probability of initiation into alcohol-abuse by heavy drinkers (ß2) are the most the parameters with the most influence on R0 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 dynamics of Gonorrhea in a structured population.

Gonorrhea is a serious global health problem due to its high incidence, with approximately 82.4 million new cases in 2020. To evaluate the consequences of targeted dynamic control of gonorrhea infection transmission, a model for gonorrhea with optimal control analysis is proposed for a structured population. The study looked at the model's positively invariant and bounded regions. The gonorrhea secondary infection expression, R0 for the structured population is computed. The maximum principle of Pontryagin is utilised to construct the optimal system for the formulated mathematical model. To reduce the continuous propagation of gonorrhea, we incorporated education, condoms usage, vaccinations, and treatment as control strategies. The numerical simulations show that the number of infections decreases when the controls are implemented. The effectiveness of the controls is shown using the efficacy plots.

Mathematical Analysis of COVID-19 Transmission Dynamics Model in Ghana with Double-Dose Vaccination and Quarantine.

The discovery of vaccines for COVID-19 has been helpful in the fight against the spread of the disease. Even with these vaccines, the virus continues to spread in many countries, with some vaccinated persons even reported to have been infected, calling for administration of booster vaccines. The need for continued use of nonpharmaceutical interventions to complement the administration of vaccines cannot therefore be overemphasized. This study presents a novel mathematical model to study the impact of quarantine and double-dose vaccination on the spread of the disease. The local stability analysis of the COVID-19-free and endemic equilibria is examined using the Lyapunov second technique. The equilibria are found to be locally asymptotically stable if ℛ 0 < 1 and ℛ 0 > 1, respectively. Besides other analytical results, numerical simulations are performed to illustrate the analytical results established in the paper.

Modeling the impact of early interventions on the transmission dynamics of coronavirus infection.

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (ß), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (µ), rate of early treatment (τ 1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

Sensitivity assessment and optimal economic evaluation of a new COVID-19 compartmental epidemic model with control interventions.

Optimal economic evaluation is pivotal in prioritising the implementation of non-pharmaceutical and pharmaceutical interventions in the control of diseases. Governments, decision-makers and policy-makers broadly need information about the effectiveness of a control intervention concerning its cost-benefit to evaluate whether a control intervention offers the best value for money. The outbreak of COVID-19 in December 2019, and the eventual spread to other parts of the world, have pushed governments and health authorities to take drastic socioeconomic, sociocultural and sociopolitical measures to curb the spread of the virus, SARS-CoV-2. To help policy-makers, health authorities and governments, we propose a Susceptible, Exposed, Asymptomatic, Quarantined asymptomatic, Severely infected, Hospitalized, Recovered, Recovered asymptomatic, Deceased, and Protective susceptible (individuals who observe health protocols) compartmental structure to describe the dynamics of COVID-19. We fit the model to real data from Ghana and Egypt to estimate model parameters using standard incidence rate. Projections for disease control and sensitivity analysis are presented using MATLAB. We noticed that multiple peaks (waves) of COVID-19 for Ghana and Egypt can be prevented if stringent health protocols are implemented for a long time and/or the reluctant behaviour on the use of protective equipment by individuals are minimized. The sensitivity analysis suggests that: the rate of diagnoses and testing, the rate of quarantine through doubling enhanced contact tracing, adhering to physical distancing, adhering to wearing of nose masks, sanitizing-washing hands, media education remains the most effective measures in reducing the control reproduction number R c , to less than unity in the absence of vaccines and therapeutic drugs in Ghana and Egypt. Optimal control and cost-effectiveness analysis are rigorously studied. The main finding is that having two controls (transmission reduction and case isolation) is better than having one control, but is economically expensive. In case only one control is affordable, then transmission reduction is better than case isolation. Hopefully, the results of this research should help policy-makers when dealing with multiple waves of COVID-19.

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.

Optimal Strategies for Control of COVID-19: A Mathematical Perspective.

A deterministic ordinary differential equation model for SARS-CoV-2 is developed and analysed, taking into account the role of exposed, mildly symptomatic, and severely symptomatic persons in the spread of the disease. It is shown that in the absence of infective immigrants, the model has a locally asymptotically stable disease-free equilibrium whenever the basic reproduction number is below unity. In the absence of immigration of infective persons, the disease can be eradicated whenever ℛ0 < 1. Specifically, if the controls u i , i=1,2,3,4, are implemented to 100% efficiency, the disease dies away easily. It is shown that border closure (or at least screening) is indispensable in the fight against the spread of SARS-CoV-2. Simulation of optimal control of the model suggests that the most cost-effective strategy to combat SARS-CoV-2 is to reduce contact through use of nose masks and physical distancing.

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 ℛVT ≤ 1, and a globally asymptotically stable endemic equilibrium ℰ1, when ℛVT > 1; and it exhibits a transcritical bifurcation at ℛVT = 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.

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.

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

A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, ℛ0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when ℛ0 < 1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin's Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.