HIV/AIDS Pandemic in Africa: Trends and Challenges

Three-quarters of the world’s AIDS population lives in Sub-Saharan Africa; most have no access to lifesaving drugs, testing facilities or even basic preventative health care. One of the major factors inhibiting medical professionals in Africa from treating this disease is the inability to access vast areas of the continent with adequately equipped medical facilities. To meet this need, Architecture for Humanity challenged the world’s architects and health care professionals to submit designs for a mobile HIV/AIDS health clinic. The pandemic is changing the demographic structure of Africa and wiping out life expectancy gains. Indeed, in many African countries, life expectancy is dropping from more than 60 years to around 45 years or even less. In this paper, we highlight the uniqueness of factors associated with HIV/AIDS pandemic in Africa and present its impact and challenges.HIV/AIDS, Africa

Modeling the Dynamics of Hepatitis C Virus and Immune System during Acute Infection

In this paper, a mathematical model on the interaction between hepatitis c virus (HCV) and immune system has been studied. The paper intends to upgrade the model developed by Avendano et al.(2002) by including death of hepatocytes due to infection and spontaneous clearance of viruses by a noncytolytic process during acute stage of the HCV infection. The next generation matrix method has been applied to compute the basic reproductive number. Also, the stability analysis of the system has been performed for the existence of the disease free and endemic equilibrium states using Meltzer matrix, Routh-Hurwitz and Lyapunov methods. The results indicate that the disease free equilibrium state is locally asymptotically stable if, and unstable if.The endemic equilibrium state is both locally and globally asymptotically stable. We calculated the sensitivity indices of the dynamic threshold relating to each parameter in the model, where we found that the decrease of the rate of infection and the rate of generation of virions have the effect of lessening the infection, which suggests that the disease can be controlled when therapeutic intervention is done on these parameters.Keywords: Hepatitis C virus, Immune system, Basic reproductive number, Disease-free equilibrium state, Endemic equilibrium state

Mathematical model for HIV and CD4+ cells dynamics in vivo

Published by International Electronic Journal of Pure and Applied Mathematics Volume 6 No. 2 2013, 83-103Mathematical models are used to provide insights into the mechanisms and dynamics of the progression of viral infection in vivo. Untangling the dynamics between HIV and CD4+ cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we develop and analyze a stochastic model for In-Host HIV dynamics that includes combined therapeutic treatment and intracellular delay between the infection of a cell and the emission of viral particles. The unique feature is that both therapy and the intracellular delay are incorporated into the model. We show the usefulness of our stochastic approach towards modeling combined HIV treatment by obtaining probability generating function, the moment structures of the healthy CD4+ cell, and the virus particles at any time t and the probability of virus clearance. Our analysis show that, when it is assumed that the drug is not completely effective, as is the case of HIV in vivo, the predicted rate of decline in plasma HIV virus concentration depends on three factors: the initial viral load before therapeutic intervention, the efficacy of therapy and the length of the intracellular delay.Mathematical models are used to provide insights into the mechanisms and dynamics of the progression of viral infection in vivo. Untangling the dynamics between HIV and CD4+ cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we develop and analyze a stochastic model for In-Host HIV dynamics that includes combined therapeutic treatment and intracellular delay between the infection of a cell and the emission of viral particles. The unique feature is that both therapy and the intracellular delay are incorporated into the model. We show the usefulness of our stochastic approach towards modeling combined HIV treatment by obtaining probability generating function, the moment structures of the healthy CD4+ cell, and the virus particles at any time t and the probability of virus clearance. Our analysis show that, when it is assumed that the drug is not completely effective, as is the case of HIV in vivo, the predicted rate of decline in plasma HIV virus concentration depends on three factors: the initial viral load before therapeutic intervention, the efficacy of therapy and the length of the intracellular delay

Bioeconomic Model for Tilapia – Nile Perch Fishery in Polluted Environment with Constant Harvesting Efforts in Tanzanian Waters of Lake Victoria

In this paper, bioeconomic model for Tilapia (Oreochromis niloticus) – Nile perch (Lates niloticus) fishery in polluted environment with the constant harvesting efforts is developed. The model analysed to get maximum sustainable yield (MSY) points and the corresponding conditions for existence established. The equilibrium points of the model found and the conditions for their existence established. The stability analysis of the interior equilibrium point is investigated by using Jacobian matrix method. Later, numerical simulations and their corresponding graphs revealed that water pollution has significant effects on the maximum sustainable yields of both Tilapia and Nile perch produces. These effects also manifests the rapid changes of species population at the interior equilibrium point. Keywords: bioeconomic model, fishery, Tilapia, Nile perch, harvesting and water pollution

Semi-Markov model for evaluating the HIV patient treatment cost

ArticleThe aim of this study is to model the progression of HIV/AIDS disease and evaluate the cost of the anti-retroviral therapy for an HIV infected patient under ART follow-up using Non homogeneous semi-Markov processes. States of the Markov process are defined by the seriousness of the sickness based on the clinical scores. The five states considered are: Asymptomatic (CD$^{+}_{4}$ count > 500 cells/microliter); Symptomatic 1 (350 < CD$^{+}_{4}$ count ≤ 500 cells/microliter); Symptomatic 2 (200 < CD$^{+}_{4}$ count ≤ 350 cells/microliter); AIDS (CD$^{+}_{4}$ count ≤ 200 cells/microliter) and Death (Absorbing state). The first four states are named as good or alive states. The models formulated can be used to gain insights on the transition dynamics of the HIV patient given the follow-up time. The transition probability Model, when fitted with data will give insights on the conditional probability of a patient moving from one disease state to another, given the current state and the follow-up time. This model will also give the probability of survival for the HIV patient under treatment given the current state and follow-up time. The total Lifetime Treatment Cost model obtained, when applied to real data will give the cost of managing an HIV patient given the starting state, the treatment combination which incurs minimum cost and which treatment combination is most effective at each state. The treatment reward model also when applied to real data will give the state, which a patient should be maintained so that they remain healthy, noninfectious and productive to the society. Also the model will show the optimal/effective time to initiate treatment, which can be used to give advice on how to handle the HIV infecteds given their states

A mathematical model for fall armyworm management on maize biomass

This research article published by Springer Nature, 2021Fall armyworm (Spodoptera frugiperda), a highly destructive and fast spreading agricultural pest native to North and South America, poses a real threat to global food security. In this paper, to explore the dynamics and implications of fall armyworm outbreak in a field of maize biomass, we propose a new dynamical system for maize biomass and fall armyworm interaction via Caputo fractional-order operator, which is not only a nonlocal operator but also contains all characteristics concerned with memory of the dynamical system. We define the basic reproduction number, which represents the average number of newborns produced by one individual female moth during its life span. We establish that the basic reproduction number is a threshold quantity, which determines persistence and extinction of the pest. Finally, we simulate the Caputo system using the Adam–Bashforth–Moulton method to illustrate the main results

Stochastic model for In-Host HIV dynamics with therapeutic intervention

Conference paper presented at “The 2nd EAUMP Conference” on 22nd – 25th August 2012. Arusha - TanzaniaMathematical models are used to provide insights into the mechanisms the dynamics between HIV and CD4+ cellular populations and molecuar interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we develop and analyze a stochastic model for In-Host HIV dynamics that includes combined therapeutic treatment and intracellular delay between the infection of a cell and the emission of viral particles, which describes HIV infection of CD4+ T-cells during therapy. The unique feature is that both therapy and the intracellular delay are incorporated into the model. Models of HIV infection that include intracellular delays are more accurate representations of the biological data. We show the usefulness of our stochastic approach towards modeling combined HIV treatment by obtaining probability distribution, variance and co-variance structures of the healthy CD4+ cell, and the virus particles at any time t. Our analysis show that, when it is assumed that the drug is not completely effective, as is the case of HIV in vivo, the predicted rate of decline in plasma HIV virus concentration depends on three factors: the death rate of the virons, the ecacy of therapy and the length of the intracellular delay.Mathematical models are used to provide insights into the mechanisms the dynamics between HIV and CD4+ cellular populations and molecuar interactions can be used to investigate the eff ective points of interventions in the HIV life cycle. With that in mind, we develop and analyze a stochastic model for In-Host HIV dynamics that includes combined therapeutic treatment and intracellular delay between the infection of a cell and the emission of viral particles, which describes HIV infection of CD4+ T-cells during therapy. The unique feature is that both therapy and the intracellular delay are incorporated into the model. Models of HIV infection that include intracellular delays are more accurate representations of the biological data. We show the usefulness of our stochastic approach towards modeling combined HIV treatment by obtaining probability distribution, variance and co-variance structures of the healthy CD4+ cell, and the virus particles at any time t. Our analysis show that, when it is assumed that the drug is not completely eff ective, as is the case of HIV in vivo, the predicted rate of decline in plasma HIV virus concentration depends on three factors: the death rate of the virons, the e cacy of therapy and the length of the intracellular delay

Stochastic Model for Langerhans cells and HIV Dynamics in Vivo

Working paperMany aspects of the complex interaction between HIV and the human immune system remain elusive. Our objective is to study these inter-actions, focusing on the specic roles of langerhans cells (LCs) in HIV infection. In patients infected with HIV, a large amount of virus is as-sociated with LCs in lymphoid tissue. To assess the influence of LCs on HIV viral dynamics during anti-retroviral therapy, we present and analyse a stochastic model describing the dynamics of HIV, CD4+ T-cells, and LCs interactions under therapeutic intervention in vivo. We per-form sensitivity analyses on the model to determine which parameters and/or which interaction mechanisms strongly affect infection dynamics.Many aspects of the complex interaction between HIV and the human immune system remain elusive. Our objective is to study these inter-actions, focusing on the speci c roles of langerhans cells (LCs) in HIV infection. In patients infected with HIV, a large amount of virus is as-sociated with LCs in lymphoid tissue. To assess the influence of LCs on HIV viral dynamics during anti-retroviral therapy, we present and analyse a stochastic model describing the dynamics of HIV, CD4+ T-cells, and LCs interactions under therapeutic intervention in vivo. We per-form sensitivity analyses on the model to determine which parameters and/or which interaction mechanisms strongly affect infection dynamics

A Deterministic Mathematical Model for the Control of Spread of Prosopis Juliflora Plants

This research article published by Journal of Mathematics and Informatics Vol. 19, 2020Prosopis juliflora plants are the most aggressive invasive species in the world. They spread by animal movement crossing from one place land to another. In this paper a deterministic model to examine the dynamics of Prosopis julifrola plants is formulated and presented by adopting a similar approach of a dynamical system as used in epidemiological modeling. The local and global stability analyses of the equilibrium points of the model performed by using next-generation for the basic reproduction number R0 computation and Lypunov function method. The finding from the study showed that the Prosopis free equilibrium of the model is both locally and globally asymptotically stable if and only if the number of secondary infections, is less than unit, that is R0 < 1. Furthermore, the study showed that there exist Prosopis endemic equilibrium for the spread when 0 R >1. The numerical simulation implemented in MATLAB ODE45 algorithm for solving linear ordinary differential equations. The study findings showed that as the number of ingested animals increase, the plant spread increases on land. Based on the findings, the study recommend the application of the model on endemic areas to improve through: Awareness on animal feeding the plant, provision of insight on plant invasion to policy makers and environmental stakeholders to include in environment framework, seminars and environment clubs by visiting community groups an educating them on plant invasion, through this the plant eradication could be achieved

Determining Important Parameters in Ebola Epidemics

The dynamics of Ebola can best be understood using a mathematical model that determines its dynamics in the community. The model designed in this study explicitly incorporates the latency period, the different transmission compartments, and immigration and emigration effects. The steady states of the system are analysed for existence of equilibria and their stability investigated. From qualitative analysis of the model, it is established that a disease-free equilibrium exists and is stable whe