MATHEMATICAL MODELING OF COMMUNICABLE IMPORTED DISEASES SCREENING IN THE UNITED ARAB EMIRATES

The United Arab Emirates (UAE), as one of the countries with high numbers of expatriates in the world, is expected to face public health challenges. The reason for this situation is that the majority of those expatriates belong to regions where health issues are usually left behind. This may create the possibility of having imported communicable diseases. However, screening policy should be tested and adapted to protect the population from any imported communicable disease. This study aims at identifying an approach and method to deal with these imported diseases via a set of differential equations. The spread of a communicable disease is examined by taking in consideration the nature of the expatriates in the UAE. The population of expatriates is divided into high risk and low risk groups. The study concluded to the possibility of the persistence of the diseases under seven possible scenarios. Each of these scenarios represents the endemic level of the disease. To clarify the case simulations of two types of diseases are examined: HIV and Tuberculosis (TB). Keywords: Basic reproduction number, stability analysis, local sensitivity analysi

신속검사가 HIV와 AIDS에 미치는 영향: 수학적 모델링

학위논문 (석사)-- 서울대학교 보건대학원 : 보건학과 보건학전공, 2016. 8. 조성일.In Korea, the cumulative number of infected cases is 9,615 by 2014, according to World Health Organization (WHO), it is, however, underestimated. To prevent this problem, testing is critical for individual to be aware of their serostatus. To enhance the effect of testing, rapid testing pilot testing started in 2014 in Seoul, Korea, it is, and however, due to the voluntary and anonymous characteristic of the testing, the effect of it has not been studied. The result has shown that when the rapid testing is only conducted in Seoul with national wide conventional testing will lead to 35% and 25% in HIV and AIDS cases in 5 years, respectively. When the rapid testing is conducted throughout Korea with national conventional testing, reduction rate for HIV and AIDS cases are 50% and 39%, respectively. Therefore, the rapid testing can be a critical factor to detect HIV/AIDS cases and proceed into reducing HIV/AIDS underestimation in KoreaChapter1.Introduction 1 1.1 Human Immunodeficiency Virus/Acquired Immune Deficiency Syndrome 1 1.2 Case Detection Methods 1 1.3 Effect of Awareness on HIV/AIDS Infection 3 1.4 Mathematical Model 4 Chapter 2. Methods 7 2.1 Methodological Overview 7 2.2 Mathematical Model 9 2.3 Parameter stability 13 2.4 Scenarios 15 2.5 Analysis 18 Chapter 3. Results 21 3.1 Parameter stability 21 3.2 Scenario 1: Equal infectivity and no test conducted 23 3.3 Scenario 2: Different infectivity and no test conducted 25 3.4 Scenario 3.1: Conventional tests only 26 3.5 Scenario 3.2 and 3.3: Rapid test in Seoul and Nationwide 28 Chapter 4. Discussion 34 Chapter 5. Conclusion 37 Reference 38 ABSTRACT (KOREAN) 41Maste

Mathematical modeling of population dynamics of HIV with antiretroviral treatment and herbal medicine

>Magister Scientiae - MScHerbal medicines have been an important part of health and wellness for hundreds of years. Recently the World Health Organization estimated that 80% of people worldwide rely on herbal medicines. Herbs contain many substances that are good for protecting the body and are therefore used in the treatment of various illnesses. Along with traditional medicines, herbs are often used in the treatment of chronic diseases such as rheumatism, migraine, chronic fatigue, asthma, eczema, and irritable bowel syndrome, among others. Herbal medicines are also applied in certain traditional communities as treatment against infectious diseases such as flu, malaria, measles, and even human immunodeficiency virus HIV-infection. Approximately 34 million people are currently infected with the human immunodeficiency virus (HIV) and 2.5 million newly infected. Therefore, HIV has become one of the major public health problems worldwide. It is important to understand the impact of herbal medicines used on HIV/AIDS. Mathematical models enable us to make predictions about the qualitative behaviour of disease outbreaks and evaluation of the impact of prevention or intervention strategies. In this dissertation we explore mathematical models for studying the effect of usage of herbal medicines on HIV. In particular we analyze a mathematical model for population dynamics of HIV/AIDS. The latter will include the impact of herbal medicines and traditional healing methods. The HIV model exhibits two steady states; a trivial steady state (HIV-infection free population) and a non-trivial steady state (persistence of HIV infection). We investigate the local asymptotic stability of the deterministic epidemic model and similar properties in terms of the basic reproduction number. Furthermore, we investigate for optimal control strategies. We study a stochastic version of the deterministic model by introducing white noise and show that this model has a unique global positive solution. We also study computationally the stochastic stability of the white noise perturbation model. Finally, qualitative results are illustrated by means of numerical simulations. Some articles from the literature that feature prominently in this dissertation are [14] of Cai et al, [10] of Bhunu et al., [86] of Van den Driessche and Watmough, [64] of Naresh et al., Through the study in this dissertation, we have prepared a research paper [1], jointly with the supervisors to be submitted for publication in an accredited journal. The author of this dissertation also contributed to the research paper [2], which close to completion. 1. Abdulaziz Y.A. Mukhtar, Peter J. Witbooi and Gail D. Hughes. A mathematical model for population dynamics of HIV with ARV and herbal medicine. 2. P.J. Witbooi, T. Seatlhodi, A.Y.A. Mukhtar, E. Mwambene. Mathematical modeling of HIV/AIDS with recruitment of infecteds

Mathematical modeling and analysis of HIV/AIDS control measures

>Magister Scientiae - MScIn this thesis, we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyse a math- ematical model that describes the dynamics of HIV infection among the im- migrant youths and intervention that can minimize or prevent the spread of the disease in the population. In particular, we are interested in the effects of public-health education and of parental care.We consider existing models of public-health education in HIV/AIDS epidemi-ology, and provide some new insights on these. In this regard we focus atten-tion on the papers [b] and [c], expanding those researches by adding sensitivity analysis and optimal control problems with their solutions.Our main emphasis will be on the effect of parental care on HIV/AIDS epidemi-ology. In this regard we introduce a new model. Firstly, we analyse the model without parental care and investigate its stability and sensitivity behaviour.We conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is asymptotically stable. Further, we use optimal control methods to determine the necessary conditions for the optimality of intervention, and for disease eradication or control. Using Pontryagin’s Maximum Principle to check the effects of screening control and parental care on the spread of HIV/AIDS, we observe that parental care is more effective than screening control. However, the most efficient control strategy is in fact a combination of parental care and screening control. The results form the central theme of this thesis, and are included in the manuscript [a] which is now being reviewed for publication. Finally, numerical simulations are performed to illustrate the analytical results

An Optimal Treatment Control of TB-HIV Coinfection

An optimal control on the treatment of the transmission of tuberculosis-HIV coinfection model is proposed in this paper. We use two treatments, that is, anti-TB and antiretroviral, to control the spread of TB and HIV infections, respectively. We first present an uncontrolled TB-HIV coinfection model. The model exhibits four equilibria, namely, the disease-free, the HIV-free, the TB-free, and the coinfection equilibria. We further obtain two basic reproduction ratios corresponding to TB and HIV infections. These ratios determine the existence and stability of the equilibria of the model. The optimal control theory is then derived analytically by applying the Pontryagin Maximum Principle. The optimality system is performed numerically to illustrate the effectiveness of the treatments

Modelling the progression of treatment scenarios in the HIV/AIDS epidemic

Advances in recent treatments for HIV/AIDS patients have shown dramatic outcomes in extending the incubation period and AIDS survival time, whilst also providing significant improvements in the quality of patients' lives. This thesis establishes a model of the HIV/AIDS epidemic that incorporates the effects of treatments, in particular, the introduction of highly active antiretroviral therapy (HAART), which became widely available during 1996. The technique of compartmental modelling is employed in an attempt to reproduce observed AIDS incidence/prevalence, HIV incidence/prevalence, and deaths from AIDS data. There are movements between compartments (sub-populations affected by the HIV/AIDS epidemic) each with an associated parameter. Each sub-population has a differential-difference equation associated with it. Once these equations have been solved numerically they give a set of steady-state solutions, from which it is possible to estimate HIV/AIDS incidence and prevalence. Some parameter values within the model are obtained from surveys, census results, etc., but others are derived using a maximum likelihood estimation (MLE) procedure. The use of realistic values gives impressive results, creating a remarkable fit with routinely collected data relating to levels of HIV/AIDS incidence and prevalence in the UK homosexual population. Finally, the model is used to project levels of incidence and prevalence over the next few years, and to investigate several possible 'what-if' scenarios, with a brief investigation into the consequent cost implications.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Modelling the progression of treatment scenarios in the HIV/AIDS epidemic

Advances in recent treatments for HIV/AIDS patients have shown dramatic outcomes in extending the incubation period and AIDS survival time, whilst also providing significant improvements in the quality of patients' lives. This thesis establishes a model of the HIV/AIDS epidemic that incorporates the effects of treatments, in particular, the introduction of highly active antiretroviral therapy (HAART), which became widely available during 1996. The technique of compartmental modelling is employed in an attempt to reproduce observed AIDS incidence/prevalence, HIV incidence/prevalence, and deaths from AIDS data. There are movements between compartments (sub-populations affected by the HIV/AIDS epidemic) each with an associated parameter. Each sub-population has a differential-difference equation associated with it. Once these equations have been solved numerically they give a set of steady-state solutions, from which it is possible to estimate HIV/AIDS incidence and prevalence. Some parameter values within the model are obtained from surveys, census results, etc., but others are derived using a maximum likelihood estimation (MLE) procedure. The use of realistic values gives impressive results, creating a remarkable fit with routinely collected data relating to levels of HIV/AIDS incidence and prevalence in the UK homosexual population. Finally, the model is used to project levels of incidence and prevalence over the next few years, and to investigate several possible 'what-if' scenarios, with a brief investigation into the consequent cost implications.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Modelling the progression of treatment scenarios in the HIV/AIDS epidemic

Advances in recent treatments for HIV/AIDS patients have shown dramatic outcomes in extending the incubation period and AIDS survival time, whilst also providing significant improvements in the quality of patients' lives. This thesis establishes a model of the HIV/AIDS epidemic that incorporates the effects of treatments, in particular, the introduction of highly active antiretroviral therapy (HAART), which became widely available during 1996. The technique of compartmental modelling is employed in an attempt to reproduce observed AIDS incidence/prevalence, HIV incidence/prevalence, and deaths from AIDS data. There are movements between compartments (sub-populations affected by the HIV/AIDS epidemic) each with an associated parameter. Each sub-population has a differential-difference equation associated with it. Once these equations have been solved numerically they give a set of steady-state solutions, from which it is possible to estimate HIV/AIDS incidence and prevalence. Some parameter values within the model are obtained from surveys, census results, etc., but others are derived using a maximum likelihood estimation (MLE) procedure. The use of realistic values gives impressive results, creating a remarkable fit with routinely collected data relating to levels of HIV/AIDS incidence and prevalence in the UK homosexual population. Finally, the model is used to project levels of incidence and prevalence over the next few years, and to investigate several possible 'what-if' scenarios, with a brief investigation into the consequent cost implications

The development of stochastic models for relative risk estimation in constructing pneumonia disease mapping in Malaysia

Pneumonia is one of the leading causes of death for infectious diseases especially in developing countries. Conventionally, its spread is only being monitored based on the total number of cases recorded without considering geographical distribution. Alternatively, disease mapping can be constructed based on the relative risk that includes a geographical distribution. A good disease mapping relies on the accuracy of relative risk estimated from the best-fitted statistical model. Therefore, this study aims to develop an alternative method in estimating the pneumonia relative risk based on four stochastic models: Susceptible-Infected-Carriers (SIC), Susceptible-Infected Recovered (SIR), Susceptible-Carrier-Infected-Recovered (SCIR), and Susceptible- Vaccinated-Carrier-Infected-Recovered (SVCIR). These estimated relative risks are then compared with those of the existing methods: Standardized Mortality Ratio (SMR), Poisson-gamma and Besag, York and Mollie (BYM) models. There are four phases in this study. Firstly, four deterministic models that are suitable for pneumonia disease transmission are selected, from which the stochastic models are developed. Next, these four stochastic models are applied to estimate the relative risk for pneumonia disease by analyzing pneumonia data in Malaysia from the year 2010 until the year 2019. The performance of these four stochastic models and existing methods is evaluated by comparing their relative risk values. Finally, the pneumonia risk maps are then constructed based on the relative risk values obtained. Findings show that there is a large gap in relative risk estimation values when using the stochastic SVCIR model compared to other models. The relative risk values when using stochastic SVCIR model decrease from high-risk level to medium risk level and from medium risk level to low-risk level. This situation occurs since stochastic SVCIR model allows for the spatial correlation between the areas and includes extra information in the model such as vaccination and carrier components. Application of the models on the Malaysian data shows that Putrajaya is identified as the highest risk of contracting pneumonia. This is because Putrajaya is the smallest area with the highest population growth rate in Malaysia. In conclusion, these stochastic models demonstrate better performance compared to the conventional models. Furthermore, these models are applicable to other infectious diseases with similar transmission characteristics. The disease mapping may assist the government in prioritizing areas that need further attention in gearing towards a sustainable health system

Mathematical model of HIV/AIDS, tuberculosis and their coevolution with optimal control: A case study in Ethiopia

The communicable disease tuberculosis (TB), human immunodeficiency virus/acquired immune deficiency syndrome (HIV/AIDS) disease, and their co-infection are the most serious public health issues in the world. In this thesis, three population level mathematical models of the three infections min Ethiopia are developed and analyzed. The first model considers the dynamics of HIV/AIDS, which comprise the following exclusive classes of individuals, the aware and unaware susceptibles, undiagnosed HIV infectious, diagnosed HIV infectious with and without AIDS symptoms, and those under HIV treatment. This model considers the rate of becoming aware and unaware as a function of media campaigns, whereas screening and treatment rates are constant. The effective reproduction number, equilibria, and nature of stability were formulated. The bifurcation occurs when the effective reproduction number is equal to unity. This model is extended to a new model which incorporates interventions such as preventive, screening, and treatment strategies. In this model, the optimal control problem is formulated and solved analytically. In addition to this, the optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Finally, the cost-effectiveness of some combined control strategies is derived. The second model reflects the TB transmission dynamics with drug resistance TB (DR-TB). The two infectious TB stages, namely drug-sensitive TB and drug-resistant TB, are considered in the model. Assuming that drug-sensitive TB can be cured by first-line anti-TB drugs. In fact, once the Tubercle Bacilli become resistant to one or more anti-TB drugs, the drug-resistance TB occurs. The model is analyzed analytically and extended to an optimal control problem via incorporating preventive efforts, case finding, and case holding. In the study, four different strategies are introduced based on different combination of measures. The optimal control problem is examined both analytically and numerically. The third model describes a new mathematical model of human immunodeficiency virus (HIV) associated with tuberculosis (TB). This full TB-HIV co-infection model is analyzed analytically. Which is extended to an optimal control problem by using controlling variables such as preventive efforts, case finding effort for TB, and HIV treatment. We proposed four strategies, which are combinations of two or more control measures at a time. The model with controls is analyzed both analytically and numerically. The numerical results are derived using the classical Runge-Kutta method of order four (RK4-method). The finding suggests that optimal combination strategies are used to reduce both the disease burden and the cost of intervention. Further, the cost- effectiveness of each strategy is assessed to identify the best cost-effective approach the fight against TB-HIV co-infection in Ethiopia.Mathematical SciencesD. Phil. (Applied Mathematics