Schistosomiasis infection is characterized by the presence of adult worms in the portal and mesenteric veins of humans as part of a complex migratory cycle initiated by cutaneous penetration of the cercariae shed by infected freshwater snails. The drug praziquantel is not always effective in the treatment against schistosomiasis at larvae stage. However, our simulations show that it is effective against mature worms and eggs. As a result, the study and understanding of immunological responses is key in understanding parasite dynamics. We therefore introduce quantitative interpretations of human immunological responses of the disease to formulate mathematical models for the within-host dynamics of schistosomiasis. We also use numerical simulations to demonstrate that it is the level of T cells that differentiates between either an effective immune response or some degree of infection. These cells are responsible for the differentiation and recruitment of eosinophils that are instrumental in clearing the parasite. From the model analysis, we conclude that control of infection is much attributed to the value of a function f, a measure of the average number of larvae penetrating a susceptible individual having hatched from an egg released by an infected individual. This agrees with evidence that there is a close association between the ecology, the distribution of infection and the disease.

Edward T. Chiyaka

Gesham Magombedze

Lawrence Mutimbu

Modelling within Host Parasite Dynamics of Schistosomiasis

We introduce a methodology based on the Luria–Delbrück fluctuation model for estimating the cell kinetics of clonally expanding populations. In particular, this approach allows estimation of the net cell proliferation rate, the extinction coefficient and the initial (viable) population size. We present a systematic approach based on spatial partitioning, which captures the local fluctuations of the number and sizes of individual clones. However, partitioning introduces measurement error by inflating the number of clones, which is dependent on time and the degree of cell migration. We perform various in silico experiments to explore the properties of the estimators and we show that there exists a direct relationship between precision and observation time. We also explore the trade-off between the measurement error and the estimation accuracy. By exploring different scales of cellular fluctuations, from the entire population down to those of individual clones, we show that this methodology is useful for inferring important parameters in neoplastic progression.

Larry W. Jean

Martin T. Suchorolski

Jihyoun Jeon

E. Georg Luebeck

Multiscale Estimation of Cell Kinetics

We investigate the potential success of the human papilloma virus (HPV) vaccine, taking into consideration possible waning immunity and the influence of behavioural parameters. We use a compartmental, population-level ordinary differential equation (ODE) model. We find the effective reproductive value for HPV, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mn>0</mml:mn><mml:mi>e</mml:mi></mml:msubsup></mml:mrow></mml:math>, which measures the threshold for infection outbreak in a population that is not entirely susceptible, together with infection prevalence. We study the effects of different parameters on both of these quantities. Results show that waning immunity plays a large part in allowing infection to persist. The proportion of the population not sexually active when vaccination occurs affects <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mn>0</mml:mn><mml:mi>e</mml:mi></mml:msubsup></mml:mrow></mml:math>, as does the rate at which individuals become sexually active. In several cases, infection persists as a result of an infection reservoir in the male cohort. To explore this further, we introduce male vaccination and find the conditions for which vaccination of males could be considered appropriate.

V. Brown

K. A. J. White

The HPV Vaccination Strategy: Could Male Vaccination Have a Significant Impact?

A deterministic compartmental sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals in heterosexual settings in which homosexuality and bisexuality issues have remained taboo is presented. We extend the model to focus on the effects of condom use as a single strategy approach in HIV prevention in the absence of any other intervention strategies. Initially, we model the use of male condoms, followed by incorporating the use of both the female and male condoms. The model includes two primary factors in condom use to control HIV which are condom efficacy and compliance. Reproductive numbers for these models are computed and compared to assess the effectiveness of male and female condom use in a community. We also extend the basic model to consider the effects of antiretroviral therapy as a single strategy. The results from the study show that condoms can reduce the number of secondary infectives and thus can slow the development of the HIV/AIDS epidemic. Further, we note from the study that treatment of AIDS patients may enlarge the epidemic when the treatment drugs are not 100&#x25; effective and when treated AIDS patients indulge in risky sexual behaviour. Thus, the treatment with amelioration of AIDS patients should be accompanied with intense public health educational programs, which are capable of changing the attitude of treated AIDS patients towards safe sex. It is also shown from the study that the use of condoms in settings with the treatment may help in reducing the number of secondary infections thus slowing the epidemic.

Noble Malunguza

Steady Mushayabasa

Christinah Chiyaka

Zindoga Mukandavire

Modelling the Effects of Condom Use and Antiretroviral Therapy in Controlling HIV/AIDS among Heterosexuals, Homosexuals and Bisexuals

We investigate a correlation between genetic diversity of hepatitis C virus population and the level of viral RNA accumulation in patient blood. Genetic diversity is defined as the mean Hamming distance between all pairs of virus RNA sequences representing the population. We have found that a low Hamming distance (i.e. low genetic diversity) correlates with a high RNA level; symmetrically, high diversity corresponds to a low RNA level. We contend that the obtained correlation strength justifies the use of the viral RNA level as a measure enabling prediction of efficiency of an established therapy. We also propose that patient qualification for therapy, based on viral RNA level, improves its efficiency.

Szymon Wasik

Paulina Jackowiak

Jacek B. Krawczyk

Pawe&#x142; Kedziora

Piotr Formanowicz

Marek Figlerowicz

Jacek B&#x142;a&#x17c;ewicz

Towards Prediction of HCV Therapy Efficiency

Pharmacokinetics (PK) has been traditionally dealt with under the homogeneity assumption. However, biological systems are nowadays comprehensively understood as being inherently fractal. Specifically, the microenvironments where drug molecules interact with membrane interfaces, metabolic enzymes or pharmacological receptors, are unanimously recognized as unstirred, space-restricted, heterogeneous and geometrically fractal. Therefore, classical Fickean diffusion and the notion of the compartment as a homogeneous kinetic space must be revisited. Diffusion in fractal spaces has been studied for a long time making use of fractional calculus and expanding on the notion of dimension. Combining this new paradigm with the need to describe and explain experimental data results in defining time-dependent rate constants with a characteristic fractal exponent. Under the one-compartment simplification this strategy is straightforward. However, precisely due to the heterogeneity of the underlying biology, often at least a two-compartment model is required to address macroscopic data such as drug concentrations. This simple modelling step-up implies significant analytical and numerical complications. However, a few methods are available that make possible the original desideratum. In fact, exploring the full range of parametric possibilities and looking at different drugs and respective biological concentrations, it may be concluded that all PK modelling approaches are indeed particular cases of the fractal PK theory.

Luis M. Pereira

Fractal Pharmacokinetics

About this journal

Computational and Mathematical Methods in Medicine publishes research and review articles focused on the application of mathematics to problems arising from the biomedical sciences.

Journal profile

Meet the editorial board

Computational and Mathematical Methods in Medicine&nbsp;maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.

Editor spotlight

Submit your proposal

Do you think there is an emerging area of research that really needs to be highlighted? Or an existing research area that has been overlooked or would benefit from deeper investigation? Raise the profile of a research area by leading a Special Issue.

Special Issues

Author guidelines

Editorial board

Databases and indexing

Computational and Mathematical Methods in Medicine - Table of contents 2010

Computational and Mathematical Methods in Medicine | Hindawi

title

Computational and Mathematical Methods in Medicine publishes research and review articles focused on the application of mathematics to problems arising from the biomedical sciences.

description

Computational and Mathematical Methods in Medicine

https://images.hindawi.com/journals/cmmm/cmmm.banner.jpg

Computational and Mathematical Methods in Medicine