Optimal control analysis of hepatocytic-erythrocytic dynamics of Plasmodium falciparum malaria.

This paper presents an in-host malaria model subject to anti-malarial drug treatment and malaria vaccine antigens combinations. Pontryagin's Maximum Principle is applied to establish optimal control strategies against infected erythrocytes, infected hepatocytes and malaria parasites. Results from numerical simulation reveal that a combination of pre-erythrocytic vaccine antigen, blood schizontocide and gametocytocide drugs would offer the best strategy to eradicate clinical P. falciparum malaria. Sensitivity analysis, further reveal that the efficacy of blood schizontocides and blood stage vaccines are crucial in the control of clinical malaria infection. Futhermore, we found that an effective blood schizontocide should be used alongside efficacious blood stage vaccine for rapid eradication of infective malaria parasites. The authors hope that the results of this study will help accelerate malaria elimination efforts by combining malaria vaccines and anti-malarial drugs against the deadly P. falciparum malaria.

Dynamics for a non-autonomous fall armyworm-maize interaction model with a saturation functional response.

In this study, we present a non-autonomous model with a Holling type II functional response, to study the complex dynamics for fall armyworm-maize biomass interacting in a periodic environment. Understanding how seasonal variations affect fall armyworm-maize dynamics is critical since maize is one of the most important cereals globally. Firstly, we study the dynamical behaviours of the basic model; that is, we investigate positive invariance, boundedness, permanence, global stability and non-persistence. We then extended the model to incorporate time dependent controls. We investigate the impact of reducing fall armyworm egg and larvae population, at minimal cost, through traditional methods and use of chemical insecticides. We noted that seasonal variations play a significant role on the patterns for all fall armyworm populations (egg, larvae, pupae and moth). We also noted that in all scenarios, the optimal control can greatly reduce the sizes of fall armyworm populations and in some scenarios, total elimination may be attained. The modeling approach presented here provides a framework for designing effective control strategies to manage the fall armyworm during outbreaks.

Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies.

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin's Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

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.

Mathematical Model for Optimal Control of Soil-Transmitted Helminth Infection.

In this paper, we study the dynamics of soil-transmitted helminth infection. We formulate and analyse a deterministic compartmental model using nonlinear differential equations. The basic reproduction number is obtained and both disease-free and endemic equilibrium points are shown to be asymptotically stable under given threshold conditions. The model may exhibit backward bifurcation for some parameter values, and the sensitivity indices of the basic reproduction number with respect to the parameters are determined. We extend the model to include control measures for eradication of the infection from the community. Pontryagian's maximum principle is used to formulate the optimal control problem using three control strategies, namely, health education through provision of educational materials, educational messages to improve the awareness of the susceptible population, and treatment by mass drug administration that target the entire population(preschool- and school-aged children) and sanitation through provision of clean water and personal hygiene. Numerical simulations were done using MATLAB and graphical results are displayed. The cost effectiveness of the control measures were done using incremental cost-effective ratio, and results reveal that the combination of health education and sanitation is the best strategy to combat the helminth infection. Therefore, in order to completely eradicate soil-transmitted helminths, we advise investment efforts on health education and sanitation controls.

Application of Optimal Control to Influenza Pneumonia Coinfection with Antiviral Resistance.

Influenza and pneumonia independently lead to high morbidity and mortality annually among the human population globally; however, a glaring fact is that influenza pneumonia coinfection is more vicious and it is a threat to public health. Emergence of antiviral resistance is a major impediment in the control of the coinfection. In this paper, a deterministic mathematical model illustrating the transmission dynamics of influenza pneumonia coinfection is formulated having incorporated antiviral resistance. Optimal control theory is then applied to investigate optimal strategies for controlling the coinfection using prevalence reduction and treatment as the system control variables. Pontryagin's maximum principle is used to characterize the optimal control. The derived optimality system is solved numerically using the Runge-Kutta-based forward-backward sweep method. Simulation results reveal that implementation of prevention measures is sufficient to eradicate influenza pneumonia coinfection from a given population. The prevention measures could be social distancing, vaccination, curbing mutation and reassortment, and curbing interspecies movement of the influenza virus.

Multiple-Strain Malaria Infection and Its Impacts on Plasmodium falciparum Resistance to Antimalarial Therapy: A Mathematical Modelling Perspective.

The emergence of parasite resistance to antimalarial drugs has contributed significantly to global human mortality and morbidity due to malaria infection. The impacts of multiple-strain malarial parasite infection have further generated a lot of scientific interest. In this paper, we demonstrate, using the epidemiological model, the effects of parasite resistance and competition between the strains on the dynamics and control of Plasmodium falciparum malaria. The analysed model has a trivial equilibrium point which is locally asymptotically stable when the parasite's effective reproduction number is less than unity. Using contour plots, we observed that the efficacy of antimalarial drugs used, the rate of development of resistance, and the rate of infection by merozoites are the most important parameters in the multiple-strain P. falciparum infection and control model. Although the drug-resistant strain is shown to be less fit, the presence of both strains in the human host has a huge impact on the cost and success of antimalarial treatment. To reduce the emergence of resistant strains, it is vital that only effective antimalarial drugs are administered to patients in hospitals, especially in malaria-endemic regions. Our results emphasize the call for regular and strict surveillance on the use and distribution of antimalarial drugs in health facilities in malaria-endemic countries.

Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance.

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number, Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lower Rc to a critical value Rc∗ for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

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.

Relationship between maternal pelvis height and other anthropometric measurements in a multisite cohort of Ugandan mothers.

INTRODUCTION: In sub Saharan Africa, childbirth remains a challenge that creates the need for additional screening tools. Maternal pelvis height, which is currently in use by automotive engineers has previously been shown to have significant associations with various childbirth related outcomes and events. This study set out to determine the associations between maternal: Age, height, weight and number of pregnancies with maternal pelvis height in Ugandan mothers. METHODS: This was a secondary analysis of maternal birth records from nine Ugandan hospitals, of mothers with singleton pregnancies. Data was analyzed using multilevel regression with respect to maternal pelvis height and additional analysis for tribe and site of childbirth intraclass correlations (ICCs). RESULTS: The mean maternal pelvis height was 7.30cm for the 2068 records. Maternal pelvis height was associated with: a 0.01cm reduction per centimeter of maternal height (P=0.02), 0.01cm increase per kg of maternal weight (P<0.01), 0.04cm increase for each additional pregnancy (P=0.03) and 0.03cm increase with respect to tribe of mother (P=0.27), for a constant of 7.97cm (P<0.01). The ICC for tribe was 0.20 (SE=0.08) and 0.37 (SE=0.11) for site. CONCLUSION: Maternal pelvis height was associated with maternal height, maternal weight and number of pregnancies. The site of childbirth had a moderate effect on the above associations with maternal pelvis height. More study on the public health screening value of these measurements in these settings is required.

Association between Maternal Pelvis Height and Intrapartum Foetal Head Moulding in Ugandan Mothers with Spontaneous Vertex Deliveries.

Introduction. In Sub-Saharan Africa, excessive foetal head moulding is commonly associated with cephalopelvic disproportion and obstructed labour. This study set out to determine the associations of maternal pelvis height and maternal height with intrapartum foetal head moulding. Methods. This was a multisite secondary analysis of maternal birth records of mothers with singleton pregnancies ending in a spontaneous vertex delivery. A summary of the details of the pregnancy and delivery records were reviewed and analysed using multilevel logistic regression respect to foetal head moulding. The alpha level was set at P < 0.05. Results. 412 records were obtained, of which 108/385 (28%) observed foetal head moulding. There was a significant reduction in risk of foetal head moulding with increasing maternal height (Adj. IRR 0.97, P = 0.05), maternal pelvis height (Adj. IRR 0.88, P < 0.01), and raptured membranes (Adj. IRR 0.10, P < 0.01). There was a significant increased risk of foetal head moulding with increasing birth weight (Adj. IRR 1.90, P < 0.01) and duration of monitored active labour (Adj. IRR 1.21, P < 0.01) in the final model. Conclusion. This study showed that increasing maternal height and maternal pelvis height were associated with a significant reduction in intrapartum foetal head moulding.

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.