Biomathematical modeling

Literature on Unified Modeling Language (UML) and aspect-orientation often focus on improving the software development process [2]. This paper presents a systems engineering perspective that motivates an aspect-oriented software architectural analysis approach using ...

This paper presents a seven-dimensional ordinary differential equation modelling the transmission of Plasmodium falciparum malaria between humans and mosquitoes with non-linear forces of infection in form of saturated incidence rates. These incidence rates produce antibodies in response to the presence of parasite-causing malaria in both human and mosquito populations.The existence of region where the model is epidemiologically feasible is established. Stability analysis of the disease-free equilibrium is investigated via the threshold parameter (reproduction number R0) obtained using the next generation matrix technique. The model results show that the disease-free equilibrium is asymptotically stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. The existence of the unique endemic equilibrium is also determined under certain conditions. Numerical simulations are carried out to confirm the analytic results and explore the possible behavior of the formulated model.

The image system for the method of regularized Stokeslets is developed and implemented. The method uses smooth localized functions to approximate a delta distribution in the derivation of the fluid flow due to a concentrated force. In order to satisfy zero-flow boundary conditions at a plane wall, the method of images derived for a standard (singular) Stokeslet is extended to give exact cancellation of the regularized flow at the wall. As the regularization parameter vanishes, the expressions reduce to the known images for singular Stokeslets. The advantage of the regularized method is that it gives bounded velocity fields even for isolated forces or for distributions of forces along curves. These are useful in the simulation of ciliary beats, flagellar motion, and particle suspensions. The expression relating force and velocity can be inverted to find the forces that generate a given velocity boundary condition. The latter is exemplified by modeling a cilium as a filament moving in a three-dimensional flow. The cilium velocity at various times is constructed from known data and used to determine the force field along the filament. Those forces can then reproduce the flow everywhere. The validity of the method is evaluated by computing the drag on a sphere moving near a wall. Comparisons with known expressions for the drag show that the method gives accurate results for spheres even within a distance from the wall equal to the surface discretization size.

We formulate and analyze Zika virus transmission model with three nonlinear forces of infection from infected mosquito, asymptomatic and symptomatic humans. The sensitivity indexes of the associated parameters of the model with respect to the basic reproduction number are calculated to identify intervention strategies for prevention and control of Zika virus. Multiple time-dependent optimal controls are considered. The analysis based on the use of optimal control theory made popular by Pontryagin's maximum principle is carried out, and the resulting optimality system is quantitatively simulated to investigate the impact of the controls on the dynamics of Zika virus. In addition, the effects of non-linearity of the forces of infection and other key parameters on the disease transmission are illustrated.

—A deterministic epidemiological model describing the spread of infectious disease characterized by pseudo-recovery due to incomplete treatment is studied. The resulting SEIRI model in a closed system is robustly analysed. Trans-critical bifurcation at the threshold, R0 = 1, is investigated and the global asymptotic dynamics of the model around the disease-free and endemic equilibria are explored by the aid of suitable Lyapunov functionals. Further, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behaviour of the system.

It is well known that ionizing radiation can cause damages to cells that interact with it directly. However, many studies have shown that damages also occur in cells that have not experienced direct interaction. This is due to the so-called bystander effect, which is observed when the irradiated cell sends signals that can damage neighboring cells. Due to the complexity of this effect, it is not easy to strictly describe it biophysically, and thus it is also difficult to simulate. This article reviews various approaches to modeling and simulating the bystander effect from the point of view of radiation biophysics. In particular, the last model presented within this article is part of a larger project of modeling the response of a group of cells to ionizing radiation using Monte Carlo methods. The new approach presented here is based on the probability tree, the Poisson distribution of signals and the saturated dose-related probability distribution of the bystander effect’s appearance, which makes the model very broad and universal.

River discharge data offer a rich source of information for reservoir management and flood control, if modelling can separate out the effects of rainfall, land use, soil type, relief, and weather conditions. In this paper, we model river discharge data from the Black Volta River, using Generalised Additive Mixed Models (GAMMs) with a space-time interaction represented via a ten-sor product of continuous time and discrete space. River discharge data from January 2000 to December 2009 for the four gauge stations along the Black Volta River namely, Lawra, Chache, Bui and Bamboi were obtained from the hydrological services department of Ghana and used for model fitting. Four GAMMs were explored, two with space-time interactions and two without space-time interactions. The comparison of the performance of the models with space-time interactions and those without space-time interactions based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) suggests that in this application, the former is better overall and in particular for modelling local variations. Further, a model with space and time main effects performed better compared with one without space and time main effects. After model selection, checking and validation, there is evidence for increasing river discharge from the most upstream gauge station to the most downstream gauge station for the study period.

In this work, a new deterministic mathematical model for a cholera carrier epidemic is developed and validated for the existence and uniqueness; hence the Lipschitz conditions are satisfied. The model threshold quantity  for the cholera dynamics is computed using next generation matrix operator approach. The model sensitivity-index of the key parameters that has influence on the basic reproduction number  is carried out. The results showed that the force of infection in the pathogen population,  with the value of  followed by the force of infection in the carrier population,  with the value of  are found to be the most sensitive parameters in the cholera prevalence and transmissions targeted for intervention and control strategies in the community. Plotted illustrations are presented to support our findings. Therefore, to curtail the spreads of cholera in the community, it is recommended that public health campaigns be conducted frequently.

Present paper envisage a model of two phased mean blood flow in human Pulmonary arterioles remote from the heart and proximate to the Lung, Keeping in view the nature of Pulmonary blood circulation in human body. The viscosity increases in the arterioles due to formation of rouleaux along axis of red blood cells. We have applied the Herschel Bulkley Non-Newtonian model in Bio- fluid mechanical setup with the help of clinical data in case of Lung Cancer for hemoglobin versus blood pressure. The overall presentation is in tensorial form and the solution technique adopted is analytical as well as numerical. The role of hematocrit is explicit in the determination of blood pressure in case of pulmonary disease Lung Cancer the graphical presentation for particular parametric value is much close to the clinical observation.

In this article, we present a mathematical six-dimensional dynamical system involving a three-tiered microbial food web without maintenance. We give a qualitative analysis of the model, and an analysis of the local stability of equilibrium points. Under general assumptions of monotonicity, we prove the uniqueness and the local stability of the positive equilibrium point corresponding to the persistence of the three bacteria. Possibilities of periodic orbits are not excluded and asymptotic coexistence is satisfied.

Vector Autoregressive (VAR) models for multivariate time series have been extensively developed and used in econometrics. However, use of VAR models outside of these areas is rather limited. This paper models the trend of flows at Bui with respect to rainfall variability and investigates whether there is any causality (Granger or instantaneous) between rainfall and flow in relation to forecasting. Monthly data on rainfall and flows from January 1954 to December 2005 was obtained from Bui Power Authority in Ghana. Both unrestricted and Bayesian VARs were estimated and compared in order to select the best VAR model for forecasting and structural analysis. The results showed that the unrestricted VAR model outperforms the Bayesian VAR model in terms of forecasting flows and rainfall at Bui. Results from the structural analysis also revealed a two-way causality from rainfall to flow and vice-versa. We conclude that modelling flows and rainfall together at Bui improves the forecasting of both of them.

A classical epidemiological framework is used to qualitatively assess the impact of early detection and treatment on the dynamics of HIV/AIDS. Within this theoretical framework, two classes of infected populations: those infected but unaware of their serological status and those who are aware of their disease status, are considered. In this context, we formulate and analyze a deterministic model for the transmission dynamics of HIV/AIDS and assess the potential population-level impact of early detection in curtailing the epidemic. A critical threshold parameter for which case detection will have a positive impact is derived. Model parameters sensitivity analysis indicates that the number of partners is the most sensitive in increasing the average number of secondary transmission parameter. However, the case detection coverage is the main drivers in reducing the initial disease transmission. Numerical simulations of the model are provided to support the analytical results. Early detection and treatment alone are insufficient to eliminate the disease, and other control strategies are to be explored.

Shiftwork may adversely impact an individual’s sleep-wake patterns and result in sleep loss (<6 h. following night shift), due to the circadian misalignment and the design of rosters and shifts. Within a mining operation, this sleep loss may have significant consequences due to fatigue, including an increased risk of accidents and chronic health conditions. This study aims to (i) determine the efficacy of an intervention that comprises a sleep education program and biofeedback through a smartphone app on sleep quality, quantity, and alertness (ii) determine the prevalence of risk for a potential sleep disorder, and (iii) quantify and describe the sleep habits and behaviors of shift workers in a remote mining operation. This study consists of a randomized controlled trial whereby eighty-eight shift workers within a remote mining operation are randomized to a control group or one of three different treatment groups that are: (i) a sleep education program, (ii) biofeedback on sleep ...

The main aim of present study is to examine a Non-Newtonian mathematical model of two phased blood flow in human pulmonary Venules, keeping in view the nature of pulmonary blood circulation. Herschel Bulkley Non-Newtonian model in Bio-fluid mechanical setup is applied with respect to the help of clinical data in case of Lung Cancer for hemoglobin versus blood pressure. In present study overall presentation is in tensorial form and the solution solution technique adopted is analytical as well as numerical. The role of hematocrit is explicit in the determination of blood pressure drop in particular circulation during pulmonary disease Lung Cancer.

Mathematical morphology (MM) is a powerful theory widely used for image processing and analysis. Distance-based morphological operators are parametrized by a reference value so that a dilation enlarges regions of an image similar to the reference while an erosion shrinks them. In this paper, we first characterize distance-based erosions, dilations, and gradients as a function of the reference. Then, assuming the reference is a sample from a random variable, we use a descriptive statistic to obtain relevant information on a certain distance-based morphological operator. We validate our approach by presenting a successful application of some statistics of distance-based morphological operators for edge detection in color images.

In this present paper was to examine a mathematical model of two phase blood flow in human pulmonary artery, keeping in view the nature of pulmonary blood circulation during Lung Cancer. The some previous researchers already assumed the blood flow to be two phase. We have apply power law model, has been transformed into biofluid mechanical set up. For the purpose, blood has been assumed to be constituted by plasma and blood cells which is realistic so far. In present study overall presentation is in tensorial form and the solution technique adopted is analytical as well as numerical. The role of Hematocrit is explicit in determination of blood pressure drop.

Resumo Em 1952, Alan Hodgkin e Andrew Huxley propuseram em um artigo como o potencial de ação é propagado ao longo do axônio de lula gigante. O modelo de Hodgkin-Huxley descreve matema-ticamente, a partir de conceitos físicos clássicos do Eletromag-netismo, como a membrana e os canais iônicos podem ser vistos como elementos de um circuito elétrico. Como os modelos pro-postos são equações diferenciais ordinárias, as soluções dessas equações podem ser complicadas de se resolver. Existem ferra-mentas matemáticas que ajudam a resolver essas equações. Nesse trabalho proponho resolver o modelo de Hodgkin-Huxley através do método de Runge-Kutta. Esse método tem a vantagem de pos-suir erro menor que o método de Euler. Com a implementação do modelo por esse método, foi obtido valores próximos da solução exata, porém o custo computacional torna cada vez mais difícil de chegar à essa solução. Palavras-chave: Neurofísica. Modelagem matemática. Equa-ções Diferenciais Ordinárias.

Abstract In 1952 Alan Hodgkin and Andrew Huxley proposed in an article how the action potential is propagated along the giant squid axon. The Hodgkin-Huxley model describes mathematically, from classical physical concepts of electromagnetism, how the membrane and ion channels can be seen as elements of an electric circuit. Since the proposed models are ordinary differential equations, the solutions of these equations can be complicated to solve. There are mathematical tools that help solve these equations. In this work I propose to solve the Hodgkin-Huxley model through the Runge-Kutta method. This method has the advantage of having less error than the Euler method. With the implementation of the model by this method, values close to the exact solution were obtained , but the computational cost makes it increasingly difficult to reach this solution.

Proposal Summary This research project is motivated from the classical treatment of Alan Turing(1952) on biological pattern formations, and the famous work of Rosenzweig-MacArthur model on multiple interacting species in Population Dynamics. This research proposal envisaged the study of global dynamics, Turing and non-Turing pattern formations of spatio-temporal reaction diffusion systems derived from Extended Rosenzweig-MacArthur model. A variant of the model with discrete delays-in-time could demonstrate the possible effect of delays on population dispersion and their pattern geome-tries outside Turing space. The project requires sophisticated dynamical tools such as maple software, finite volume discretization of the model, results from elliptic Partial Differential Equations, and Topological Degree Theory to derive propositions and their numerical simulations.

Human papillomavirus (HPV) has been identified as the main etiological factor in the developing of cervical cancer (CC). This finding has propitiated the development of vaccines that help to prevent the HPVs 16 and 18 infection. Both genotypes are associated with 70% of CC worldwide. In the present study, we aimed to determine the emergence of high-risk nonvaccine HPV after actual vaccination scheme to estimate the impact of the current HPV vaccines. A SIR-type model was used to study the HPV dynamics after vaccination. According to the results, our model indicates that the application of the vaccine reduces infection by target or vaccine genotypes as expected. However, numerical simulations of the model suggest the presence of the phenomenon called vaccineinduced pathogen strain replacement. Here, we report the following replacement mechanism: if the effectiveness of cross-protective immunity is not larger than the effectiveness of the vaccine, then the high-risk nonvaccine genotypes emerge. In this scenario, further studies of infection dispersion by HPV are necessary to ascertain the real impact of the current vaccines, primarily because of the different high-risk HPV types that are found in CC.

We studied macroscopic ion currents from macrophages and compared their patterns of behavior using classical and fractal analysis. Peak and steady state currents were measured respectively at the beginning and end of a voltage-clamp pulse. Hurst coefficients H and fractional dimensions were calculated for the current fluctuations (I H ) during the intervening interval; these fluctuations are usually assumed to be white noise. We show that I H is different from 0.5 and that the increments are stationary, indicating that the dynamic model has memory and that the intervening current fluctuations cannot be considered as white noise. I H is less than 0.5, implying an antipersistent pattern. In addition, we show that the relation between inactivation and I H versus voltage V fit an equation I H (V) = f(V, α, m, d), where α is associated with fractional calculus and m and d are free parameters. Fitting by a fractional model confirms that the phenomenon has memory.

"""The vector--bias model of malaria transmission, recently proposed by Chamchod and Britton, is considered. Nonlinear stability analysis is performed by means of the Lyapunov theory and the
LaSalle Invariance Principle. The classical threshold for the basic reproductive number, $R_0$, is obtained: if $R_0>1$, then the disease will spread and persist within its host population. If $R_0<1$, then the disease will die out. Then, the model has been extended to incorporate both immigration and disease--induced death of humans. This modification has been shown to strongly affect the system dynamics. In particular, by using the theory of center manifold, the occurrence of a backward bifurcation at $R_0=1$ is shown possible. This implies that a stable endemic equilibrium may also exists for $R_0<1$. When $R_0>1$, the endemic persistence of the disease has been proved to hold also
for the extended model. This last result is obtained by means of the geometric approach to global stability.

Highlights

► We consider two models for the spread of malaria in human and mosquito populations. ► The models consider the greater attractiveness of infectious humans to mosquitoes. ► The extended version incorporates immigration and disease-induced death of humans. ► We perform the global stability analysis for both the original and the extended model. ► We prove that a backward bifurcation may occur for the extended model at R_0=1.

Keywords:  Malaria; Mathematical model; Stability; Lyapunov function; Bifurcations"""

A classical epidemiological framework is used to qualitatively assess the impact of early detection and treatment on the dynamics of HIV/AIDS. Within this theoretical framework, two classes of infected populations: those infected but unaware of their serological status and those who are aware of their disease status, are considered. In this context, we formulate and analyze a deterministic model for the transmission dynamics of HIV/AIDS and assess the potential population-level impact of early detection in curtailing the epidemic. A critical threshold parameter for which case detection will have a positive impact is derived. Model parameters sensitivity analysis indicates that the number of partners is the most sensitive in increasing the average number of secondary transmission parameter. However, the case detection coverage is the main drivers in reducing the initial disease transmission. Numerical simulations of the model are provided to support the analytical results. Early detection and treatment alone are insufficient to eliminate the disease, and other control strategies are to be explored.

Induction and proliferation of cancer cells are complex processes whose ab initio mathematical description is virtually impossible. Nevertheless, some integral characteristics such as the Gompertz law, which is generally used to describe cancer development, can result from a simple mathematical consideration of biophysical processes. The simplified response to a single-source lesion created in a cell's DNA consists in the repair of the lesion or induction of a mutation which can lead to neoplastic transformation. This approach makes it possible to propose a single mathematical formula connecting the Gompertz curve with the simplified biophysical characteristics of tumor growth. Such an approach, which merges the process of neoplastic transformation with cancer development, is shown in the present paper based on the relatively simple analytical and Monte-Carlo models. The models operate with a small number of biophysical parameters and account, at least in part, for the mechanisms that operate in an organism exposed to low doses of ionizing radiation.

Tissue engineering constructs and other solid implants with biomedical applications, such as drug delivery devices or bioartificial organs, need oxygen (O 2 ) to function properly. To understand better the vascular integration of such devices, we recently developed a novel model sensor containing O 2 -sensitive crystals, consisting of a polymeric capsule limited by a nano-porous filter. The sensor was implanted in mice with hydrogel alone (control) or hydrogel embedded with mouse CD117/c-kit+ bone marrow progenitor cells (BMPC) in order to stimulate peri-implant neovascularization. The sensor provided local partial O 2 pressure (pO 2 ) using non-invasive electron paramagnetic resonance (EPR) signal measurements. A consistently higher level of per-implant oxygenation was observed in the cell-treatment case as compared to the control over a 10-week period. In order to provide a mechanistic explanation of these experimental observations, we present in this paper a mathematical model, formulated as a system of coupled partial differential equations, that simulates peri-implant vascularization. In the control case, vascularization is considered to be the result of a Foreign Body Reaction (FBR) while in the cell-treatment case, adipogenesis in response to paracrine stimuli produced by the stem cells is assumed to induce neovascularization. The model is validated by fitting numerical predictions of local pO 2 to measurements from the implanted sensor. The model is then used to investigate further the potential for using stem cell treatment to enhance the vascular integration of biomedical implants. We thus demonstrate how mathematical modeling combined with experimentation can be used to infer how vasculature develops around biomedical implants in control and stem celltreated cases.