Modelling the impact of stigmatisation of Ebola survivors on the disease transmission dynamics.

Ebola virus disease (EVD) is one of the most highly stigmatised diseases in any affected country because of the disease's high infectivity and case fatality rate. Infected individuals and most especially survivors are often stigmatised by their communities for fear of contagion. We propose and analyse a mathematical model to examine the impact of stigmatisation of Ebola survivors on the disease dynamics. The model captures both the internal stigmatisation experienced by infected individuals after witnessing survivors being stigmatised and the external stigmatisation imposed on survivors by their communities. The results obtained from our analysis and simulations show that both internal and external stigma may lead to an increase in the burden of Ebola virus disease by sustaining the number of infected individuals who hide their infection and the number of unsafe burials of deceased Ebola victims. Strategies that seek to put an end to both forms of stigmatisation and promote safe burials will therefore go a long way in averting the EVD burden.

Application of optimal control to the dynamics of COVID-19 disease in South Africa.

SARS-CoV-2 (COVID-19) belongs to the beta-coronavirus family, which include: the severe acute respiratory syndrome coronavirus (SARS-CoV) and the Middle East respiratory syndrome coronavirus (MERS-CoV). Since its outbreak in South Africa in March 2020, it has lead to high mortality and thousands of people contracting the virus. Mathematical analysis of a model without controls was done and the basic reproduction number ( R 0 ) of the COVID-19 for the South African pandemic determined. Permissible controls were introduced and an optimal control problem using the Pontraygain Maximum Principle is formulated. Numerical findings suggest that joint implementation of effective mask usage, physical distancing and active screening and testing, are effective measures to curtail the spread of the disease in the human population. The results obtained in this paper are of public health importance in the control and management of the spread for the novel coronavirus, SARS-CoV-2, in South Africa.

Modelling the potential role of media campaigns on the control of Listeriosis.

Human Listeria infection is a food-borne disease caused by the consumption of contaminated food products by the bacterial pathogen, Listeria. In this paper, we propose a mathematical model to analyze the impact of media campaigns on the spread and control of Listeriosis. The model exhibited three equilibria namely; disease-free, Listeria-free and endemic equilibria. The food contamination threshold is determined and the local stability analyses of the model is discussed. Sensitivity analysis is done to determine the model parameters that most affect the severity of the disease. Numerical simulations were carried out to assess the role of media campaigns on the Listeriosis spread. The results show that; an increase in the intensity of the media awareness campaigns, the removal rate of contaminated food products, a decrease in the contact rate of Listeria by humans results in fewer humans getting infected, thus leading to the disease eradication. An increase in the depletion of media awareness campaigns results in more humans being infected with Listeriosis. These findings may significantly impact policy and decision-making in the control of Listeriosis disease.

An Ebola virus disease model with fear and environmental transmission dynamics.

•Due to its high case fatality rate, EVD undoubtedly instills fear in the inhabitants of any affected community.•We propose an Ebola model with fear, which considers the pathogens in the environment to quantify the effect of fear and environmental transmission on the EVD disease dynamics.•The fear of death from Ebola is proportional to the Ebola disease transmission rate.•At high levels of fear, the number of EVD cases decrease.

Modelling the Potential Impact of Social Distancing on the COVID-19 Epidemic in South Africa.

The novel coronavirus (COVID-19) pandemic continues to be a global health problem whose impact has been significantly felt in South Africa. With the global spread increasing and infecting millions, containment efforts by countries have largely focused on lockdowns and social distancing to minimise contact between persons. Social distancing has been touted as the best form of response in managing a rapid increase in the number of infected cases. In this paper, we present a deterministic model to describe the impact of social distancing on the transmission dynamics of COVID-19 in South Africa. The model is fitted to data from March 5 to April 13, 2020, on the cumulative number of infected cases, and a scenario analysis on different levels of social distancing is presented. The model shows that with the levels of social distancing under the initial lockdown level between March 26 and April 13, 2020, there would be a projected continued rise in the number of infected cases. The model also looks at the impact of relaxing the social distancing measures after the initial announcement of the lockdown. It is shown that relaxation of social distancing by 2% can result in a 23% rise in the number of cumulative cases whilst an increase in the level of social distancing by 2% would reduce the number of cumulative cases by about 18%. The model results accurately predicted the number of cases after the initial lockdown level was relaxed towards the end of April 2020. These results have implications on the management and policy direction in the early phase of the epidemic.

Assessing the potential impact of limited public health resources on the spread and control of typhoid.

Typhoid fever is a systemic infection caused by Salmonella Typhi and occurs predominantly in association with poor sanitation and lack of clean drinking water. Despite recent progress in water and sanitation coverage, the disease remains a substantial public health problem in many developing countries. A mathematical model for the spread of typhoid has been formulated using non linear ordinary differential equations. The model includes a special treatment function to assess the effects of limited treatment resources on the spread of typhoid. It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation whose implications are discussed. The results suggest the need for comprehensive and accessible treatment facilities to curtail typhoid infection.

Modelling the role of correctional services on gangs: insights through a mathematical model.

Research has shown that gang membership increases the chances of offending, antisocial behaviour and drug use. Gang membership should be acknowledged as part of crime prevention and policy designs, and when developing interventions and preventative programmes. Correctional services are designed to rehabilitate convicted offenders. We formulate a deterministic mathematical model using nonlinear ordinary differential equations to investigate the role of correctional services on the dynamics of gangs. The recruitment into gang membership is assumed to happen through an imitation process. An epidemic threshold value, [Formula: see text], termed the gang reproduction number, is proposed and defined herein in the gangs' context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that gangs may persist in the population even if [Formula: see text] is less than one. Sensitivity analysis of [Formula: see text] was performed to determine the relative importance of different parameters in gang initiation. The critical efficacy ε* is evaluated and the implications of having functional correctional services are discussed.

On the Role of Imitation on Adolescence Methamphetamine Abuse Dynamics.

Adolescence methamphetamine use is an issue of considerable concern due to its correlation with later delinquency, divorce, unemployment and health problems. Understanding how adolescents initiate methamphetamine abuse is important in developing effective prevention programs. We formulate a mathematical model for the spread of methamphetamine abuse using nonlinear ordinary differential equations. It is assumed that susceptibles are recruited into methamphetamine use through imitation. An epidemic threshold value, [Formula: see text], termed the abuse reproduction number, is proposed and defined herein in the drug-using context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that methamphetamine problems may persist in the population even if [Formula: see text] is less than one. Sensitivity analysis of [Formula: see text] was performed to determine the relative importance of different parameters in methamphetamine abuse initiation. The model is then fitted to data on methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse in the treatment centres of Cape Town and parameter values that give the best fit are chosen. Results show that the proportion of methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse will continue to decrease in Cape Town of South Africa. The results suggest that intervention programs targeted at reducing adolescence methamphetamine abuse, are positively impacting methamphetamine abuse.

Modelling Drug Abuse Epidemics in the Presence of Limited Rehabilitation Capacity.

The abuse of drugs is now an epidemic globally whose control has been mainly through rehabilitation. The demand for drug abuse rehabilitation has not been matched with the available capacity resulting in limited placement of addicts into rehabilitation. In this paper, we model limited rehabilitation through the Hill function incorporated into a system of nonlinear ordinary differential equations. Not every member of the community is equally likely to embark on drug use, risk structure is included to help differentiate those more likely (high risk) to abuse drugs and those less likely (low risk) to abuse drugs. It is shown that the model has multiple equilibria, and using the centre manifold theory, the model exhibits the phenomenon of backward bifurcation whose implications to rehabilitation are discussed. Sensitivity analysis and numerical simulations are performed. The results show that saturation in rehabilitation will in the long run lead to the escalation of drug abuse. This means that limited access to rehabilitation has negative implications in the fight against drug abuse where rehabilitation is the main form of control. This suggests that increased access to rehabilitation is likely to lower the drug abuse epidemic.

Modelling the dynamics of two political parties in the presence of switching.

This paper generalizes the model proposed by Misra, by considering switching between political parties. In the model proposed, the movements of members from political party B to political party C and vice versa, are considered but the net movement is considered by assuming that [Formula: see text] (a constant), which implies that the movement of members is either from party B to party C or from party C to party B. In this paper we remodel these movements through switching functions to capture how individuals switch between parties. The results provide a more comprehensive synopsis of the dynamics between two political parties.

Exploring the benefits of antibody immune response in HIV-1 infection using a discrete model.

The role of antibodies in HIV-1 infection is investigated using a discrete-time mathematical model that considers cell-free and cell-associated transmission of the virus. Model analysis shows that the effect of each type of antibody is dependent on the stage of the infection. Neutralizing antibodies are efficient in controlling the viral levels in the early days after seroconversion and antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication are efficient when the infection becomes established. Model simulations show that antibodies that inhibit viral replication are more effective in controlling the infection than those that recruit Natural Killer T cells after infection establishment. The model was fitted to subjects of the Tsedimoso study conducted in Botswana and conclusions similar to elasticity analysis results were obtained. Model fitting results predicted that neutralizing antibodies are more efficient in controlling the viral levels than antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication in the early days after seroconversion.

Modelling the trends of inpatient and outpatient rehabilitation for methamphetamine in the Western Cape province of South Africa.

BACKGROUND: Dependence on methamphetamine remains one of the major health and social problem in the Western Cape province of South Africa. We consider a mathematical model that takes into account two forms of rehabilitation, namely; inpatient and outpatient. We examine the trends of these two types of rehabilitation. We also seek to investigate the global dynamics of the developed methamphetamine epidemic model. METHODS: The model is designed by likening the initiation process to an infection that spreads in a community through interactions between methamphetamine users and non-users. We make use of Lyapunov functions obtained from a suitable combination of common quadratic and Volterra-type functions to establish the global stability of the methamphetamine-persistent steady state. The least squares curve fit routine (lsqcurvefit) in Matlab with optimization is used to estimate the parameter values. RESULTS: The model analysis shows that the model has two equilibria, the methamphetamine free equilibrium and the methamphetamine persistent equilibrium, that are both globally stable when the threshold R(a) < 1 and R(a) > 1, respectively. Upon fitting the model to data on drug users under rehabilitation, parameter values that give the best fit were obtained. The projections carried out the long term trends of these forms of rehabilitation. CONCLUSION: The results suggest that inpatient rehabilitation programs have an increased potential of enhancing the chances of recovery for methamphetamine addicts.

The Implications of HIV Treatment on the HIV-Malaria Coinfection Dynamics: A Modeling Perspective.

Most hosts harbor multiple pathogens at the same time in disease epidemiology. Multiple pathogens have the potential for interaction resulting in negative impacts on host fitness or alterations in pathogen transmission dynamics. In this paper we develop a mathematical model describing the dynamics of HIV-malaria coinfection. Additionally, we extended our model to examine the role treatment (of malaria and HIV) plays in altering populations' dynamics. Our model consists of 13 interlinked equations which allow us to explore multiple aspects of HIV-malaria transmission and treatment. We perform qualitative analysis of the model that includes positivity and boundedness of solutions. Furthermore, we evaluate the reproductive numbers corresponding to the submodels and investigate the long term behavior of the submodels. We also consider the qualitative dynamics of the full model. Sensitivity analysis is done to determine the impact of some chosen parameters on the dynamics of malaria. Finally, numerical simulations illustrate the potential impact of the treatment scenarios and confirm our analytical results.

Modelling Optimal Control of Cholera in Communities Linked by Migration.

A mathematical model for the dynamics of cholera transmission with permissible controls between two connected communities is developed and analysed. The dynamics of the disease in the adjacent communities are assumed to be similar, with the main differences only reflected in the transmission and disease related parameters. This assumption is based on the fact that adjacent communities often have different living conditions and movement is inclined toward the community with better living conditions. Community specific reproduction numbers are given assuming movement of those susceptible, infected, and recovered, between communities. We carry out sensitivity analysis of the model parameters using the Latin Hypercube Sampling scheme to ascertain the degree of effect the parameters and controls have on progression of the infection. Using principles from optimal control theory, a temporal relationship between the distribution of controls and severity of the infection is ascertained. Our results indicate that implementation of controls such as proper hygiene, sanitation, and vaccination across both affected communities is likely to annihilate the infection within half the time it would take through self-limitation. In addition, although an infection may still break out in the presence of controls, it may be up to 8 times less devastating when compared with the case when no controls are in place.

Modelling HIV/AIDS in the presence of an HIV testing and screening campaign.

Preventing and managing the HIV/AIDS epidemic in South Africa will dominate the next decade and beyond. Reduction of new HIV infections by implementing a comprehensive national HIV prevention programme at a sufficient scale to have real impact remains a priority. In this paper, a deterministic HIV/AIDS model that incorporates condom use, screening through HIV counseling and testing (HCT), regular testing and treatment as control strategies is proposed with the objective of quantifying the effectiveness of HCT in preventing new infections and predicting the long-term dynamics of the epidemic. It is found that a backward bifurcation occurs if the rate of screening is below a certain threshold, suggesting that the classical requirement for the basic reproduction number to be below unity though necessary, is not sufficient for disease control in this case. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number R(0). Numerical simulations are performed and the model is fitted to data on HIV prevalence in South Africa. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long-term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed.

Modelling hospitalization, home-based care, and individual withdrawal for people living with HIV/AIDS in high prevalence settings.

In sub-Saharan Africa, the model of care for people who are living with HIV/AIDS has changed from hospital care to home-based care. In this paper, a mathematical model describing the dynamics of HIV transmission, hospitalization, and home-based care is constructed and analysed. The model reproduction number R(e) is determined and discussed. The equilibria are determined and analysed in terms of R(e). It is shown that if R(e)<1, the disease free equilibrium is both locally and globally asymptotically stable. The model has a unique endemic equilibrium and is locally asymptotically stable whenever R(e)>1. Five cases arise in the discussion of R(e) pertaining to intervention strategies. Numerical simulations are done to compare the impact of each strategy on the dynamics of HIV/AIDS. The model is fitted to the prevalence data estimates from UNAIDS on Zimbabwe. The implications of some key epidemiological parameters are investigated numerically. Projections are made to determine the possible long term trends of the prevalence of HIV in Zimbabwe.