Modeling the Impact of Seasonal Weather Variations on the Infectiology of Brucellosis.

A deterministic mathematical model for brucellosis that incorporates seasonality on direct and indirect transmission parameters for domestic ruminants, wild animals, humans, and the environment was formulated and analyzed in this paper. Both analytical and numerical simulations are presented. From this study, the findings show that variations in seasonal weather have the great impact on the transmission dynamics of brucellosis in humans, livestock, and wild animals. Thus, in order for the disease to be controlled or eliminated, measures should be timely implemented upon the fluctuation in the transmission of the disease.

Mathematical Modelling of HIV-HCV Coinfection Dynamics in Absence of Therapy.

Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency virus (HIV), 6.3% are coinfected with hepatitis C virus (HCV). Coinfection with HIV reduces the chance of HCV spontaneous clearance. In this work, we formulated and analysed a deterministic model to study the HIV and HCV coinfection dynamics in absence of therapy. Due to chronic stage of HCV infection being long, asymptomatic, and infectious, our model formulation was based on the splitting of the chronic stage into the following: before onset of cirrhosis and its complications and after onset of cirrhosis. We computed the basic reproduction numbers using the next generation matrix method. We performed numerical simulations to support the analytical results. We carried out sensitivity analysis to determine the relative importance of the different parameters influencing the HIV-HCV coinfection dynamics. The findings reveal that, in the long run, there is a substantial number of individuals coinfected with HIV and latent HCV. Therefore, HIV and latently HCV-infected individuals need to seek early treatment so as to slow down the progression of HIV to AIDS and latent HCV to advanced HCV.

Modelling Optimal Control of In-Host HIV Dynamics Using Different Control Strategies.

HIV is one of the major causes of deaths, especially in Sub-Saharan Africa. In this paper, an in vivo deterministic model of differential equations is presented and analyzed for HIV dynamics. Optimal control theory is applied to investigate the key roles played by the various HIV treatment strategies. In particular, we establish the optimal strategies for controlling the infection using three treatment regimes as the system control variables. We have applied Pontryagin's Maximum Principle in characterizing the optimality control, which then has been solved numerically by applying the Runge-Kutta forth-order scheme. The numerical results indicate that an optimal controlled treatment strategy would ensure significant reduction in viral load and also in HIV transmission. It is also evident from the results that protease inhibitor plays a key role in virus suppression; this is not to underscore the benefits accrued when all the three drug regimes are used in combination.

Plague disease model with weather seasonality.

The plague disease model that include the effect of seasonal weather variation in its transmission is investigated in this paper. The disease is caused by an extremely virulent bacteria Yersinia pestis named after a French bacteriologist Alexandre Yersin. The analysis shows that, when the periodic reproduction number (RT) is greater than one there exist a globally asymptotically stable disease free equilibrium solution (DFS). Using fundamental existence-uniqueness theorem we were able to prove the existence of positive periodic solutions. The analysis further shows that when RT > 1 then there is at least one positive periodic solution. We additionally establish the conditions for global stability of periodic solutions of the model and finally using numerical simulation we depict the behavioral dynamics of plague disease and justify the theoretical solutions.

Modelling hepatotoxicity and antiretroviral therapeutic effect in HIV/HBV coinfection.

Enzyme alanine aminotransferase (ALT) elevation which reflects hepatocellular injury is a current challenge in people infected with human immunodeficiency virus (HIV) on antiretroviral therapy (ART). One of the factors that enhance the risk of hepatotoxicity is underlying diseases such as hepatitis caused by hepatitis B virus (HBV). HIV/HBV coinfected patients stand a greater risk of hepatotoxicity because all ART are toxic and liver cells (hepatocytes) that are responsible for metabolising the toxic ART, support all stages of HIV and HBV viral production. Mathematical models coupled with numerical simulations are used in this study with the aim of investigating the optimal combination of ART in HIV/HBV coinfection. Emtricitabine, tenofovir and efavirenz is the optimal combination that maximises the therapeutic effect of therapy and minimises the toxic response to medication in HIV/HBV coinfection.

The In Vivo Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells.

The in vivo dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having R0 < 1. Lastly, the biological dynamics of HIV in vivo infection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral replication. In addition, the results emphasize the importance of developing controls, interventions, and management policies that when implemented would lead to viral suppression during acute infection.

Characterizing plasma albumin concentration changes in TB/HIV patients on anti retroviral and anti -tuberculosis therapy.

PURPOSE: Plasma albumin, a biomarker for hepatic function, is reported to correspondingly decrease in concentration as disease severity increases in chronic infections including HIV and TB. Our objective was to develop a semi-mechanistic disease progression model to quantify plasma albumin concentration changes during TB and HIV therapy and identify the associated covariate factors. METHODS: Plasma albumin concentration data was collected at specified times for 3 months from 262 HIV participants receiving efavirenz based anti retroviral therapy. Of these, 158 were TB co-infected and on Rifampicin based anti -tuberculosis co-treatment. An indirect response model with zero order albumin production and first order elimination was developed in NONMEM version 7.2 to describe our data. Genotype (CYP2B6*6 and 11, CYP3A5, ABCB1c.3435C>T and ABCB1rs), TB disease status, baseline age, body weight, plasma creatinine, alanine transaminase enzyme and CD4(+) count were the potential model covariates tested. RESULTS: The proposed model successfully described plasma albumin concentration changes in the study population. There was a 10.9% and 48.6% increase in albumin production rates in HIV only and TB co-infected participants respectively. Participants co-infected with TB showed a 44.2% lower baseline albumin secretion rate than those without TB while ABCB1c.3435C>T mutation was associated with a 16% higher steady state albumin secretion rate following treatment. CONCLUSION: A semi-mechanistic model describes plasma albumin concentration changes in HIV patients on ART. Further work is required to establish the utility of the model in monitoring disease progression and predicting prognosis in HIV and TB co-infected patients in absence of or during treatment.

Modeling the impact of climate change on the dynamics of Rift Valley Fever.

A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was considered to compute the basic reproduction number ℛ 0 and investigate the impact of temperature and precipitation on ℛ 0. To study the effect of model parameters to ℛ 0, sensitivity and elasticity analysis of ℛ 0 were performed. When temperature and precipitation effects are not considered, ℛ 0 is more sensitive to the expected number of infected Aedes spp. due to one infected livestock and more elastic to the expected number of infected livestock due to one infected Aedes spp. When climatic data are used, ℛ 0 is found to be more sensitive and elastic to the expected number of infected eggs laid by Aedes spp. via transovarial transmission, followed by the expected number of infected livestock due to one infected Aedes spp. and the expected number of infected Aedes spp. due to one infected livestock for both regions Arusha and Dodoma. These results call for attention to parameters regarding incubation period, the adequate contact rate of Aedes spp. and livestock, the infective periods of livestock and Aedes spp., and the vertical transmission in Aedes species.

Mathematical modeling of liver enzyme elevation in HIV mono-infection.

HIV-infected individuals are increasingly becoming susceptible to liver disease and, hence, liver-related mortality is on a rise. The presence of CD4+ in the liver and the presence of C-X-C chemokine receptor type 4 (CXCR4) on human hepatocytes provide a conducive environment for HIV invasion. In this study, a mathematical model is used to analyse the dynamics of HIV in the liver with the aim of investigating the existence of liver enzyme elevation in HIV mono-infected individuals. In the presence of HIV-specific cytotoxic T-lymphocytes, the model depicts a unique endemic equilibrium with a transcritical bifurcation when the basic reproductive number is unity. Results of the study show that the level of liver enzyme alanine aminotransferase (ALT) increases with increase in the rate of hepatocytes production. Numerical simulations reveal significant elevation of alanine aminotransferase with increase in viral load. The findings presuppose that while liver damage in HIV infection has mostly been associated with HIV/HBV coinfection and use of antiretroviral therapy (ART), it is possible to have liver damage solely with HIV infection.

The dynamics, causes and possible prevention of Hepatitis E outbreaks.

Rapidly spreading infectious diseases are a serious risk to public health. The dynamics and the factors causing outbreaks of these diseases can be better understood using mathematical models, which are fit to data. Here we investigate the dynamics of a Hepatitis E outbreak in the Kitgum region of northern Uganda during 2007 to 2009. First, we use the data to determine that R0 is approximately 2.25 for the outbreak. Secondly, we use a model to estimate that the critical level of latrine and bore hole coverages needed to eradicate the epidemic is at least 16% and 17% respectively. Lastly, we further investigate the relationship between the co-infection factor for malaria and Hepatitis E on the value of R0 for Hepatitis E. Taken together, these results provide us with a better understanding of the dynamics and possible causes of Hepatitis E outbreaks.