A Mathematical Model for the Transmission and Spread of Drug Sensitive and Resistant Malaria Strains within a Human Population

Malaria remains by far the world's most important tropical disease, killing more people than any other communicable disease. A number of preventive and control measures have been put in place and most importantly drug treatment. The emergence of drug resistance against the most common and affordable antimalarials is widespread and poses a key obstacle to malaria control. A mathematical model that incorporates evolution of drug resistance and treatment as a preventive strategy is formulated and analyzed. The qualitative analysis of the model is given in terms of the effective reproduction number, Re. The existence and stability of the disease-free and endemic equilibria of the model are studied. We establish the threshold parameters below which the burden due to malaria can be brought under control. Numerical simulations are done to determine the role played by key parameters in the model. The public health implications of the results are twofold; firstly every effort should be taken to minimize the evolution of drug resistance due to treatment failure and secondly high levels of treatment and development of immunity are essential in reducing the malaria burden.

Computational Simulations of Flow and Oxygen/Drug Delivery in a Three-Dimensional Capillary Network

A computational fluid dynamics (CFD) model is developed to simulate the flow and delivery of oxygen and other substances in a capillary network. A three-dimensional capillary network has been constructed to replicate the one studied by Secomb et al. (2000), and the computational framework features a non-Newtonian viscosity model of blood and the oxygen transport model including in-stream oxygen-hemoglobin dissociation and wall flux due to tissue absorption, as well as an ability to study delivery of drugs and other materials in the capillary streams. The model is first run to compute the volumetric flow rates from the velocity profiles in the segments and compared with Secomb’s work with good agreement. Effects of abnormal pressure and stenosis conditions, as well as those arising from different capillary configurations, on the flow and oxygen delivery are investigated, along with a brief look at the unsteady effects and drug dispersion in the capillary network. The current approach allows for inclusion of oxygen and other material transports, including drugs, nutrients, or contaminants based on the flow simulations. Also, three-dimensional models of complex circulatory systems ranging in scale from macro- to microvascular vessels, in principle, can be constructed and analyzed in detail using the current method.

A Note on Hypertension Classification Scheme and Soft Computing Decision Making System

Nowadays young professionals are a soft target of hypertension due to the increased work pressure and poor tolerance. Many people have high blood pressure for years without knowing it. Most of the time, there are no symptoms, but when this condition goes untreated it damages arteries and vital organs throughout the body and that is why it is also termed as the silent killer. Complications arising from hypertension could lead to stroke and heart failure. Soft computing approach provides a sharper conclusion from vague, ambiguous, and imprecise data (generally found in medical field) using linguistic variables. In this study, a soft computing diagnostic support system for the risk assessment of hypertension is proposed.

Total Variation Filtered Demons for Improved Registration of Sliding Organs

We present a new approach to regularize the displacement field of the accelerated Demons registration algorithm. The accelerated Demons algorithm uses Gaussian smoothing to penalize oscillatory motion in the displacement fields during registration. This regularization approach is often applied and ensures a smooth deformation field. However, when registering images with discontinuities in their motion field such as from organs sliding along the chest wall, the assumption of a smooth deformation field is invalid. In this work, we propose using total variation based smoothing that is known to better retain the discontinuities in the deformation field. The proposed approach is a first step towards automatically recovering breathing induced organ motion with good accuracy.

Thermal Distribution of Ultrasound Waves in Prostate Tumor: Comparison of Computational Modeling with In Vivo Experiments

Ultrasound irradiation to a certain site of the body affects the efficacy of drug delivery through changes in the permeability of cell membrane. Temperature increase in irradiated area may be affected by frequency, intensity, period of ultrasound, and blood perfusion. The aim of present study is to use computer simulation and offer an appropriate model for thermal distribution profile in prostate tumor. Moreover, computer model was validated by in vivo experiments. Method. Computer simulation was performed with COMSOL software. Experiments were carried out on prostate tumor induced in nude mice (DU145 cell line originated from human prostate cancer) at frequency of 3 MHz and intensities of 0.3, 0.5, and 1 w/cm2 for 300 seconds. Results. Computer simulations showed a temperature rise of the tumor for the applied intensities of 0.3, 0.5 and 1 w/cm2 of 0.8, 0.9, and 1.1°C, respectively. The experimental data carried out at the same frequency demonstrated that temperature increase was 0.5, 0.9, and 1.4°C for the above intensities. It was noticed that temperature rise was very sharp for the first few seconds of ultrasound irradiation and then increased moderately. Conclusion. Obtained data holds great promise to develop a model which is able to predict temperature distribution profile in vivo condition.

Confidence Intervals for the Mean Based on Exponential Type Inequalities and Empirical Likelihood

For independent observations, recently, it has been proposed to construct the confidence intervals for the mean using exponential type inequalities. Although this method requires much weaker assumptions than those required by the classical methods, the resulting intervals are usually too large. Still in special cases, one can find some advantage of using bounded and unbounded Bernstein inequalities. In this paper, we discuss the applicability of this approach for dependent data. Moreover, we propose to use the empirical likelihood method both in the case of independent and dependent observations for inference regarding the mean. The advantage of empirical likelihood is its Bartlett correctability and a rather simple extension to the dependent case. Finally, we provide some simulation results comparing these methods with respect to their empirical coverage accuracy and average interval length. At the end, we apply the above described methods for the serial analysis of a gene expression (SAGE) data example.

Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge

This paper describes a prey-predator model with Holling type II functional response incorporating constant prey refuge and harvesting to both prey and predator species. We have analyzed the boundedness of the system and existence of all possible feasible equilibria and discussed local as well as global stabilities at interior equilibrium of the system. The occurrence of Hopf bifurcation of the system is examined, and it was observed that the bifurcation is either supercritical or subcritical. Influences of prey refuge and harvesting efforts are also discussed. Some numerical simulations are carried out for the validity of theoretical results.

Fluctuations Analysis of Finite Discrete Birth and Death Chains with Emphasis on Moran Models with Mutations

The Moran model is a discrete-time birth and death Markov chain describing the evolution of the number of type 1 alleles in a haploid population with two alleles whose total size N is preserved during the course of evolution. Bias mechanisms such as mutations or selection can affect its neutral dynamics. For the ergodic Moran model with mutations, we get interested in the fixation probabilities of a mutant, the growth rate of fluctuations, the first hitting time of the equilibrium state starting from state {0}, the first return time to the equilibrium state, and the first hitting time of {N} starting from {0}, together with the time needed for the walker to reach its invariant measure, again starting from {0}. For the last point, an appeal to the notion of Siegmund duality is necessary, and a cutoff phenomenon will be made explicit. We are interested in these problems in the large population size limit N→∞. The Moran model with mutations includes the heat exchange models of Ehrenfest and Bernoulli-Laplace as particular cases; these were studied from the point of view of the controversy concerning irreversibility (H-theorem) and the recurrence of states.

An Overview of Multiple Sequence Alignments and Cloud Computing in Bioinformatics

Multiple sequence alignment (MSA) of DNA, RNA, and protein sequences is one of the most essential techniques in the fields of molecular biology, computational biology, and bioinformatics. Next-generation sequencing technologies are changing the biology landscape, flooding the databases with massive amounts of raw sequence data. MSA of ever-increasing sequence data sets is becoming a significant bottleneck. In order to realise the promise of MSA for large-scale sequence data sets, it is necessary for existing MSA algorithms to be run in a parallelised fashion with the sequence data distributed over a computing cluster or server farm. Combining MSA algorithms with cloud computing technologies is therefore likely to improve the speed, quality, and capability for MSA to handle large numbers of sequences. In this review, multiple sequence alignments are discussed, with a specific focus on the ClustalW and Clustal Omega algorithms. Cloud computing technologies and concepts are outlined, and the next generation of cloud base MSA algorithms is introduced.

Optimal Control of an SIR Model with Delay in State and Control Variables

We will investigate the optimal control strategy of an SIR epidemic model with time delay in state and control variables. We use a vaccination program to minimize the number of susceptible and infected individuals and to maximize the number of recovered individuals. Existence for the optimal control is established; Pontryagin’s maximum principle is used to characterize this optimal control, and the optimality system is solved by a discretization method based on the forward and backward difference approximations. The numerical simulation is carried out using data regarding the course of influenza A (H1N1) in Morocco. The obtained results confirm the performance of the optimization strategy.