Occurrence of HIV eradication for preexposure prophylaxis treatment with a deterministic HIV model

The authors examine the human immunodeficiency virus (HIV) eradication in this study using a mathematical model and analyse the occurrence of virus eradication during the early stage of infection. To this end they use a deterministic HIV-infection model, modify it to describe the pharmacological dynamics of antiretroviral HIV drugs, and consider the clinical experimental results of preexposure prophylaxis HIV treatment. They also use numerical simulation to model the experimental scenario, thereby supporting the clinical results with a model-based explanation. The study results indicate that the protocol employed in the experiment can eradicate HIV in infected patients at the early stage of the infection

Applications of Mathematical Modelling in Oncolytic Virotherapy and Immunotherapy

Cancer is a devastating disease that touches almost everyone and finding effective treatments presents a highly complex problem, requiring extensive multidisciplinary research. Mathematical modelling can provide insight into both cancer formation and treatment. A range of techniques are developed in this thesis to investigate two promising therapies: oncolytic virotherapy, and combined oncolytic virotherapy and immunotherapy. Oncolytic virotherapy endeavours to eradicate cancer cells by exploiting the aptitude of virus-induced cell death. Building on this premise, combined oncolytic virotherapy and immunotherapy aims to harness and stimulate the immune system's inherent ability to recognise and destroy cancerous cells. Using deterministic and agent-based mathematical modelling, perturbations of treatment characteristics are investigated and optimal treatment protocols are suggested. An integro differential equation with distributed parameters is developed to characterise the function of the E1B genes in an oncolytic adenovirus. Subsequently, by using a bifurcation analysis of a coupled-system of ordinary differential equations for oncolytic virotherapy, regions of bistability are discovered, where increased injections can result in either tumour eradication or tumour stabilisation. Through an extensive hierarchical optimisation to multiple data sets, drawn from in vitro and in vivo modelling, gel-release of a combined oncolytic virotherapy and immunotherapy treatment is optimised. Additionally, using an agent-based modelling approach, delayed-infection of an intratumourally administered virus is shown to be able to reduce tumour burden. This thesis develops new mathematical models that can be applied to a range of cancer therapies and suggests engineered treatment designs that can significantly advance current therapies and improve treatments

The stability analyses of the mathematical models of hepatitis C virus infection

There are two mathematical models of Hepatitis C virus (HCV) being discussed; the original model of HCV viral dynamics (Neumann et al., 1998) and its extended model (Dahari et al., 2007). The key aspects of the mathematical models have provided resources for analysing the stability of the uninfected and the infected steady states, in evaluating the antiviral effectiveness of therapy and for estimating the ranges of values of the parameters for clinical treatment. The original model is considered to be a deterministic model because of the predictive nature of the antiviral therapy within the constant target cells. Numerical simulations are carried out in the extended model, to explain the stability of the steady states in the absence or existence of migration in hepatocytes and, drug efficacy in treating HCV infection

Trends in Infectious Diseases

This book gives a comprehensive overview of recent trends in infectious diseases, as well as general concepts of infections, immunopathology, diagnosis, treatment, epidemiology and etiology to current clinical recommendations in management of infectious diseases, highlighting the ongoing issues, recent advances, with future directions in diagnostic approaches and therapeutic strategies. The book focuses on various aspects and properties of infectious diseases whose deep understanding is very important for safeguarding human race from more loss of resources and economies due to pathogens

Immune Response in the Study of Infectious Diseases (Co-Infection) in an Endemic Region

abstract: Diseases have been part of human life for generations and evolve within the population, sometimes dying out while other times becoming endemic or the cause of recurrent outbreaks. The long term influence of a disease stems from different dynamics within or between pathogen-host, that have been analyzed and studied by many researchers using mathematical models. Co-infection with different pathogens is common, yet little is known about how infection with one pathogen affects the host's immunological response to another. Moreover, no work has been found in the literature that considers the variability of the host immune health or that examines a disease at the population level and its corresponding interconnectedness with the host immune system. Knowing that the spread of the disease in the population starts at the individual level, this thesis explores how variability in immune system response within an endemic environment affects an individual's vulnerability, and how prone it is to co-infections. Immunology-based models of Malaria and Tuberculosis (TB) are constructed by extending and modifying existing mathematical models in the literature. The two are then combined to give a single nine-variable model of co-infection with Malaria and TB. Because these models are difficult to gain any insight analytically due to the large number of parameters, a phenomenological model of co-infection is proposed with subsystems corresponding to the individual immunology-based model of a single infection. Within this phenomenological model, the variability of the host immune health is also incorporated through three different pathogen response curves using nonlinear bounded Michaelis-Menten functions that describe the level or state of immune system (healthy, moderate and severely compromised). The immunology-based models of Malaria and TB give numerical results that agree with the biological observations. The Malaria--TB co-infection model gives reasonable results and these suggest that the order in which the two diseases are introduced have an impact on the behavior of both. The subsystems of the phenomenological models that correspond to a single infection (either of Malaria or TB) mimic much of the observed behavior of the immunology-based counterpart and can demonstrate different behavior depending on the chosen pathogen response curve. In addition, varying some of the parameters and initial conditions in the phenomenological model yields a range of topologically different mathematical behaviors, which suggests that this behavior may be able to be observed in the immunology-based models as well. The phenomenological models clearly replicate the qualitative behavior of primary and secondary infection as well as co-infection. The mathematical solutions of the models correspond to the fundamental states described by immunologists: virgin state, immune state and tolerance state. The phenomenological model of co-infection also demonstrates a range of parameter values and initial conditions in which the introduction of a second disease causes both diseases to grow without bound even though those same parameters and initial conditions did not yield unbounded growth in the corresponding subsystems. This results applies to all three states of the host immune system. In terms of the immunology-based system, this would suggest the following: there may be parameter values and initial conditions in which a person can clear Malaria or TB (separately) from their system but in which the presence of both can result in the person dying of one of the diseases. Finally, this thesis studies links between epidemiology (population level) and immunology in an effort to assess the impact of pathogen's spread within the population on the immune response of individuals. Models of Malaria and TB are proposed that incorporate the immune system of the host into a mathematical model of an epidemic at the population level.Dissertation/ThesisPh.D. Applied Mathematics for the Life and Social Sciences 201

Biomathematics of Chlamydia

Chlamydia trachomatis (C. trachomatis) related sexually transmitted infections are a major global public health concern. C. trachomatis afflict millions of men, women, and children worldwide and frequently result in serious medical diseases. In this thesis, mathematical modeling is applied in order to comprehend the dynamics of Chlamydia pathogens within host, their interactions with the immune systems, behavior in the presence of other pathogens, transmission dynamics in a human population, and the efficacy of control measures. The thesis begins with a brief introduction of the bacteria Chlamydia in Chapter 1. In Chapter 2, we give a brief detail of the mathematical modeling of infectious diseases, and its specific application to study the pathogen. In Chapter 3, a linear delay differential compartmental model is developed, and its special application is shown for a laboratory experiment conducted to study the intracellular development cycle of Chlamydia. The delay accounts for the time spent by bacteria in their various forms and for the time taken to go through the replication cycle. The mathematical model tracks the number of Chlamydia infected cells at each stage of the cell division cycle. Moreover, the formula for the final size of each compartment is derived. With initial conditions taken from the experiment, the model is fitted to results from the laboratory data. This simple linear model is capable of reflecting the outcomes of the laboratory experiment. In Chapter 4, at a population level, a novel mathematical model is introduced to study the dynamics of the co-infection between C. trachomatis, and herpes simplex virus (HSV). The concept of the model is based on the observation that in an individual simultaneously infected with both pathogens, the presence of HSV will make the Chlamydia persistent. In its persistent phase, Chlamydia is not replicating and is non-infectious. Important threshold parameters are obtained for the persistence of both infections. We prove global stability results for the disease-free and the boundary equilibria by applying the theory of asymptotically autonomous systems. Further, the model is calibrated to disease parameters to determine the population prevalence of both diseases and compare it with epidemiological findings. In Chapter 5, a compartmental maturity structured model is developed to investigate an optimal control problem for the treatment of chronic Chlamydia infection. The model takes into account the interaction of the pathogens with the immune system and its effects on the formation of persistent Chlamydia particles. As the system takes the form of a mixed ODE-PDE system, the results of the conventional form of Pontryagin’s maximal principle for ordinary differential equations are not suitable. For our purpose, we construct an optimal control problem for a general maturity compartmental model, and hence it consists of ordinary and partial differential equations, moreover, the boundary conditions are also nonlinear. For a fixed control, we verify the existence, uniqueness, and boundedness of the solutions. The system is numerically simulated for a variety of cost functions in order to calculate the optimal treatment for curing Chlamyida infection. We believe that since our findings were validated for a general model with maturity structure, they may be applied to any specific compartmental model that is compatible with the established system

Periodicity of epidemics of invasive disease due to infection with Streptococcus pneumoniae in the United States

Despite the availability of vaccines, every year 40,000 individuals die due to the direct effect of Invasive Pneumococcal Disease (IPD) or its complications. IPD has been associated with 100,000-135,000 hospitalizations for pneumonia, 57,000 cases of bacteremia, and 300 cases of meningitis in the United States every year. Little is known about IPD epidemic patterns beyond annual seasonality, and this lack of understanding has limited the ability to detect early changes in IPD epidemiology that may lead to large outbreaks. To mitigate this gap in understanding, a retrospective cohort design study was conducted using a population-based cohort from the National Hospital Discharge Survey for the period 1979-2006. This study set out to determine whether invasive infection by S. pneumoniae in the United States occurs in an epidemic pattern of a predictable recurrent nature and definable frequency. The theoretical basis for the study was drawn from the dynamic modeling of stochastic epidemic systems, and the analysis utilized time-series methods to examine the data. These analyses lead to the finding that IPD epidemics demonstrate a chaotic dynamic and a discrete, non-Markov process; that is, there is no predictable pattern to epidemics of IPD. The results of this study, that recurrent events consistent with periodic epidemics could not be identified, provide support for the current method of IPD surveillance and existing models of IPD dynamics. The present practice of mass vaccination by risk group, as opposed to vaccination for a predicted outbreak, is supported by the results of this study. These evidence-supported interventions will yield significant reductions in the morbidity and mortality associated with IPD, and the positive social change that results from improved health outcomes, reductions in suffering, and decreased health care costs

In silico modelling of in-host tuberculosis dynamics : towards building the virtual patient

Tuberculosis (TB) accounts for over 1 million deaths each year, despite effective treatment regimens being available. Improving the treatment of TB will require new regimens, each of which will need to be put through expensive and lengthy clinical trials, with no guarantee of success. The ability to predict which of many novel regimens to progress through the clinical trial stages would be an important tool to TB research. as current models are constrained in their ability to reflect the whole spectrum of pathophysiology, particularly as there remains uncertainty around the events that occur. This thesis explores the use of computational techniques to model a pulmonary human TB infection. We introduce the first in silico model of TB occurring over the whole lung that incorporates both the environmental heterogeneity that is exhibited within different spatial regions of the organ, and the different bacterial dissemination routes, in order to understand how bacteria move during infection and why post-primary disease is typically localised towards the apices of the lung. Our results show that including environmental heterogeneity within the lung can have profound effects on the results of an infection, by creating a region towards the apex which is preferential for bacterial proliferation. We also present a further iteration of the model, whereby the environment is made more granular to better understand the regions which are afflicted during infection, and show how sensitivity analysis can determine the factors that contribute most to disease outcomes. We show that in order to simulate TB disease within a human lung with sufficient accuracy, better understanding of the dynamics is required. The model presented in this thesis is intended to provide insight into these complicated dynamics, and thus make progress towards an end goal of a virtual clinical trial, consisting of a heterogeneous population of synthetic virtual patients."“This work was supported by the PreDiCT TB consortium (IMI Joint undertaking grant agreement number 115337, resources of which are composed of financial contribution from the European Union’s Seventh Framework Programme (FP7/2007-2013) and EF-PIA companies’ in kind contribution.)” -- Acknowledgement