Search results for: compartmental model

Authors: Jessemyn Modiini, Timothy Lynar, Elena Sitnikova

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We present a novel enhanced compartmental model for malware spread analysis in cyber security. This paper applies cyber security data features to epidemiological compartmental models to model the infectious potential of malware. Compartmental models are most efficient for calculating the infectious potential of a disease. In this paper, we discuss and profile epidemiologically relevant data features from a Domain Name System (DNS) dataset. We then apply these features to epidemiological compartmental models to network traffic features. This paper demonstrates how epidemiological principles can be applied to the novel analysis of key cybersecurity behaviours and trends and provides insight into threat modelling above that of kill-chain analysis. In applying deterministic compartmental models to a cyber security use case, the authors analyse the deficiencies and provide an enhanced stochastic model for cyber epidemiology. This enhanced compartmental model (SUEICRN model) is contrasted with the traditional SEIR model to demonstrate its efficacy.

Keywords: cybersecurity, epidemiology, cyber epidemiology, malware

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Authors: M. Mousavi-Daramoroudi, H. Yousefnia, F. Abbasi-Davani, S. Zolghadri

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In this study, ¹⁷⁷Lu-DOTATOC was prepared under optimized conditions (radiochemical purity: > 99%, radionuclidic purity: > 99%). The percentage of injected dose per gram (%ID/g) was calculated for organs up to 168 h post injection. Compartmental model was applied to mathematical description of the drug behaviour in tissue at different times. The biodistribution data showed the significant excretion of the radioactivity from the kidneys. The adrenal and pancreas, as major expression sites for somatostatin receptor (SSTR), had significant uptake. A pharmacokinetic model of ¹⁷⁷Lu-DOTATOC was presented by compartmental analysis which demonstrates the behavior of the complex.

Keywords: biodistribution, compartmental modeling, ¹⁷⁷Lu, Octreotide

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Authors: M. Mousavi-Daramoroudi, H. Yousefnia, F. Abbasi-Davani, S. Zolghadri

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Dosimetry is an indispensable and precious factor in patient treatment planning to minimize the absorbed dose in vital tissues. In this study, compartmental model was used in order to estimate the human absorbed dose of ¹⁷⁷Lu-DOTATOC from the biodistribution data in wild type rats. For this purpose, ¹⁷⁷Lu-DOTATOC was prepared under optimized conditions and its biodistribution was studied in male Syrian rats up to 168 h. Compartmental model was applied to mathematical description of the drug behaviour in tissue at different times. Dosimetric estimation of the complex was performed using radiation absorbed dose assessment resource (RADAR). The biodistribution data showed high accumulation in the adrenal and pancreas as the major expression sites for somatostatin receptor (SSTR). While kidneys as the major route of excretion receive 0.037 mSv/MBq, pancreas and adrenal also obtain 0.039 and 0.028 mSv/MBq. Due to the usage of this method, the points of accumulated activity data were enhanced, and further information of tissues uptake was collected that it will be followed by high (or improved) precision in dosimetric calculations.

Keywords: compartmental modeling, human absorbed dose, ¹⁷⁷Lu-DOTATOC, Syrian rats

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Authors: M. S. Mousavi-Daramoroudi, H. Yousefnia, S. Zolghadri, F. Abbasi-Davani

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Dosimetry is an indispensable and precious factor in patient treatment planning; to minimize the absorbed dose in vital tissues. In this study, In accordance with the proper characteristics of DOTATOC and ¹⁷⁷Lu, after preparing ¹⁷⁷Lu-DOTATOC at the optimal conditions for the first time in Iran, radionuclidic and radiochemical purity of the solution was investigated using an HPGe spectrometer and ITLC method, respectively. The biodistribution of the compound was assayed for treatment of adenocarcinoma breast cancer in bearing BALB/c mice. The results have demonstrated that ¹⁷⁷Lu-DOTATOC is a profitable selection for therapy of the tumors. Because of the vital role of internal dosimetry before and during therapy, the effort to improve the accuracy and rapidity of dosimetric calculations is necessary. For this reason, a new method was accomplished to calculate the absorbed dose through mixing between compartmental model, animal dosimetry and extrapolated data from animal to human and using MIRD method. Despite utilization of compartmental model based on the experimental data, it seems this approach may increase the accuracy of dosimetric data, confidently.

Keywords: ¹⁷⁷Lu-DOTATOC, biodistribution modeling, compartmental model, internal dosimetry

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Authors: Amadou Banda Ndione, Charles Awono Onana

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In this paper the compartmental approach is applied to build a macroeconomic model characterized by countries. We consider a total of N countries that are subdivided into three compartments according to their economic status: D(t) denotes the compartment of developing countries at time t, E(t) stands for the compartment of emerging countries at time t while A(t) represents advanced countries at time t. The model describes the process of economic development and includes the notion of openness through collaborations between countries. Two delays appear in this model to describe the average time necessary for collaborations between countries to become efficient for their development process. Our model represents the different stages of development. It further gives the conditions under which a country can change its economic status and demonstrates the short-term positive effect of openness on economic growth. In addition, we investigate bifurcation by considering the delay as a bifurcation parameter and examine the onset and termination of Hopf bifurcations from a positive equilibrium. Numerical simulations are provided in order to illustrate the theoretical part and to support discussion.

Keywords: compartmental systems, delayed dynamical system, economic development, fiscal policy, hopf bifurcation

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Authors: Karla E. Sanchez-Cazares, Kim H. Parker, Jennifer H. Tweedy

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The purpose of this work is to develop a simple compartmental model of cerebral fluid balance including blood and cerebrospinal-fluid (CSF). At the first level the cerebral arteries and veins are modelled as bifurcating trees with constant scaling factors between generations which are connected through a homogeneous microcirculation. The arteries and veins are assumed to be non-rigid and the cross-sectional area, resistance and mean pressure in each generation are determined as a function of blood volume flow rate. From the mean pressure and further assumptions about the variation of wall permeability, the transmural fluid flux can be calculated. The results suggest the next level of modelling where the cerebral vasculature is divided into three compartments; the large arteries, the small arteries, the capillaries and the veins with effective compliances and permeabilities derived from the detailed vascular model. These vascular compartments are then linked to other compartments describing the different CSF spaces, the cerebral ventricles and the subarachnoid space. This compartmental model is used to calculate the distribution of fluid in the cranium. Known volumes and flows for normal conditions are used to determine reasonable parameters for the model, which can then be used to help understand pathological behaviour and suggest clinical interventions.

Keywords: cerebrovascular, compartmental model, CSF model, vascular network

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Authors: Mahdieh Jajroudi

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Developing a pharmacokinetic model for the neuroendocrine tumors therapy agent 177Lu-DOTATATE in nude mice bearing AR42J rat pancreatic tumor to investigate and evaluate the behavior of the complex was the main purpose of this study. The utilization of compartmental analysis permits the mathematical differencing of tissues and organs to become acquainted with the concentration of activity in each fraction of interest. Biodistribution studies are onerous and troublesome to perform in humans, but such data can be obtained facilely in rodents. A physiologically based pharmacokinetic model for scaling up activity concentration in particular organs versus time was developed. The mathematical model exerts physiological parameters including organ volumes, blood flow rates, and vascular permabilities; the compartments (organs) are connected anatomically. This allows the use of scale-up techniques to forecast new complex distribution in humans' each organ. The concentration of the radiopharmaceutical in various organs was measured at different times. The temporal behavior of biodistribution of 177Lu labeled somatostatin analogues was modeled and drawn as function of time. Conclusion: The variation of pharmaceutical concentration in all organs is characterized with summation of six to nine exponential terms and it approximates our experimental data with precision better than 1%.

Keywords: biodistribution modeling, compartmental analysis, 177Lu labeled somatostatin analogues, neuroendocrine tumors

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Authors: Muleya Nqobile, Winston Garira

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We presented a compartmental deterministic multi-scale model which encompass internal plant defensive mechanism and pathogen interaction, then we consider nesting the model into the epidemiological model. The objective was to improve our understanding of the transmission dynamics of within host and between host of Guignardia citricapa Kiely. The inflow of infected class was scaled down to individual level while the outflow was scaled up to average population level. Conceptual model and mathematical model were constructed to display a theoretical framework which can be used for predicting or identify disease pattern.

Keywords: epidemiological model, mathematical modelling, multi-scale modelling, immunological model

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Authors: Asrat M.Belachew, Tiago Pereira, Institute of Mathematics, Computer Sciences, Avenida Trabalhador São Carlense, 400, São Carlos, 13566-590, Brazil

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Infectious diseases are among the most prominent threats to human beings. They cause morbidity and mortality to an individual and collapse the social, economic, and political systems of the whole world collectively. Mathematical models are fundamental tools and provide a comprehensive understanding of how infectious diseases spread and designing the control strategy to mitigate infectious diseases from the host population. Modeling the spread of infectious diseases using a compartmental model of inhomogeneous populations is good in terms of complexity. However, in the real world, there is a situation that accounts for heterogeneity, such as ages, locations, and contact patterns of the population which are ignored in a homogeneous setting. In this work, we study how classical an SEIR infectious disease spreading of the compartmental model can be extended by incorporating the mobility of population between heterogeneous cities during an outbreak of infectious disease. We have formulated an SEIR multi-cities epidemic spreading model using a system of 4k ordinary differential equations to describe the disease transmission dynamics in k-cities during the day and night. We have shownthat the model is epidemiologically (i.e., variables have biological interpretation) and mathematically (i.e., a unique bounded solution exists all the time) well-posed. We constructed the next-generation matrix (NGM) for the model and calculated the basic reproduction number R0for SEIR-epidemic spreading model with cities mobility. R0of the disease depends on the spectral radius mobility operator, and it is a threshold between asymptotic stability of the disease-free equilibrium and disease persistence. Using the eigenvalue perturbation theorem, we showed that sending a fraction of the population between cities decreases the reproduction number of diseases in interconnected cities. As a result, disease transmissiondecreases in the population.

Keywords: SEIR-model, mathematical model, city mobility, epidemic spreading

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Authors: T. G. Kassem, A. K. Adunchezor, J. P. Chollom

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This paper describes a mathematical model developed to predict the dynamics of Hepatitis B virus (HBV) infection and to evaluate the potential impact of vaccination and treatment on its dynamics. We used a compartmental model expressed by a set of differential equations based on the characteristic of HBV transmission. With these, we find the threshold quantity R0, then find the local asymptotic stability of disease free equilibrium and endemic equilibrium. Furthermore, we find the global stability of the disease free and endemic equilibrium.

Keywords: hepatitis B virus, epidemiology, vaccination, mathematical model

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Authors: Hakiki Kheira, Belhamiti Omar

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In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Keywords: Caputo derivative, epidemiology, Legendre wavelet method, obesity

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Authors: Charlene N. T. Mfangnia, Henri Tonnang, Berge Tsanou, Jeremy Herren

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The Microsporidia MB found in the populations of anopheles is a recently discovered symbiont responsible for the Plasmodium transmission blocking. From early studies, it was established that the symbiont can be transmitted vertically and horizontally. The present study uses compartmental mathematical modelling approach to investigate the dynamics of Microsporidia transmission in the mosquito population with the mindset of establishing a mechanism for use to control malaria. Data and information obtained from laboratory experiments are used to estimate the model parameters with and without temperature dependency of mosquito traits. We carry out the mathematical analysis focusing on the equilibria states and their stability for the autonomous model. Through the modelling experiments, we are able to assess and confirm the contribution of vertical and horizontal transmission in the proliferation of Microsporidia MB in the mosquito population. In addition, the basic and target reproductions are computed, and some long-term behaviours of the model, such as the local (and global) stability of equilibrium points, are rigorously analysed and illustrated numerically. We establish the conditions responsible for the low prevalence of the symbiont-infected mosquitoes observed in nature. Moreover, we identify the male death rate, the mating rate and the attractiveness of MB-positive mosquitoes as mosquito traits that significantly influence the spread of Microsporidia MB. Furthermore, we highlight the influence of temperature in the establishment and persistence of MB-infected mosquitoes in a given area.

Keywords: microsporidia MB, vertical transmission, horizontal transmission, compartmental modelling approach, temperature-dependent mosquito traits, malaria, plasmodium-transmission blocking

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Authors: Nader Al-Rashidi, David Greenhalgh

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Mathematical modelling techniques are now being used by health organizations worldwide to help understand the likely impact that intervention strategies treatment options and combinations of these have on the prevalence and incidence of hepatitis C virus (HCV) in the people who inject drugs (PWID) population. In this poster, we develop a deterministic, compartmental mathematical model to approximate the spread of the HCV in a PWID population that has been divided into two groups by time since onset of injection. The model assumes that after injection needles adopt the most infectious state of their previous state or that of the PWID who last injected with them. Using analytical techniques, we find that the model behaviour is determined by the basic reproductive number R₀, where R₀ = 1 is a critical threshold separating two different outcomes. The disease-free equilibrium is globally stable if R₀ ≤ 1 and unstable if R₀ > 1. Additionally, we make some simulations where have confirmed that the model tends to this endemic equilibrium value with realistic parameter values giving an HCV prevalence.

Keywords: hepatitis C, people who inject drugs, HCV, PWID

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Authors: Benjamin Aina Peter, Amos Wale Ogunsola

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In this paper, a mathematical model of malaria transmission was presented with the effect of seasonal shift, due to global fluctuation in temperature, on the increase of conveyor of the infectious disease, which probably alters the region transmission potential of malaria. A deterministic compartmental model was proposed and analyzed qualitatively. Both qualitative and quantitative approaches of the model were considered. The next-generation matrix is employed to determine the basic reproduction number of the model. Equilibrium points of the model were determined and analyzed. The numerical simulation is carried out using Excel Micro Software to validate and support the qualitative results. From the analysis of the result, the optimal temperature for the transmission of malaria is between and . The result also shows that an increase in temperature due to seasonal shift gives rise to the development of parasites which consequently leads to an increase in the widespread of malaria transmission in Kampala. It is also seen from the results that an increase in temperature leads to an increase in the number of infectious human hosts and mosquitoes.

Keywords: seasonal variation, indoor residual spray, efficacy of spray, temperature-dependent model

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Authors: Dhivya Arumugam, Kaliyappan Thananjeyan

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The monomer of (3-((4-(methacryloyloxy)phenylimino)methyl)-2-hydroxybenzoic acid) schiff base polymer was prepared by reacting methacryloyl chloride with imine compound derived from 3-formylsalisylic acid and 4- aminophenol. The monomer was polymerized in DMF at 70oC using benzoyl peroxide as free radical initiator. Polymer metal complex was obtained in DMF solution of polymer with aqueous solution of metal ions. The polymer and the polymer metal complex were characterized by elemental analysis and spectral studies. The elemental analysis data suggest that the metal to ligand ratio is 1:1 and hence, it acts as a binucleating compartmental ligand. The IR spectral data of these complexes suggest that the metals are coordinated through nitrogen of the imine group, the oxygen of carboxylate ion and the oxygen of the phenolic –OH group which also acts as the bridging ligand. The electronic spectra and magnetic moments of the polychelates shows that octahedral and square planar structure for Ni(II) and Cu(II) complexes respectively. X-ray diffraction studies revealed that polychelates are highly crystalline. The thermal and electrical properties, catalytic activity, structure property relationships are discussed. Further the synthesized polymer was used for metal uptake studies from waste water, which is one of the effective waste water treatment strategies. And also, the polymers and polychelates were investigated for antimicrobial activity with various microorganisms by using agar well diffusion method and the results have been discussed.

Keywords: acyclic compartmental ligands, binucleating ligand, 3-formylsalicylic acid, free radical polymerization, polluting ions, polychelate

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Authors: S. Zolghadri, M. Mousavi-Daramoroudi, H. Yousefnia, F. Abbasi-Davani

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In this study, the absorbed dose of human organs after injection of ¹⁷⁷Lu-DOTATOC was studied based on the biodistribution of the complex in adenocarcinoma breast cancer bearing mice. For this purpose, the biodistribution of the radiolabelled complex was studied and compartmental modeling was applied to calculate the absorbed dose with high precision. As expected, ¹⁷⁷Lu-DOTATOC illustrated a notable specific uptake in tumor and pancreas, organs with high level of somatostatin receptor on their surface and the effectiveness of the radio-conjugate for targeting of the breast adenocarcinoma tumors was indicated. The elicited results of modeling were the exponential equations, and those are utilized for obtaining the cumulated activity data by taking their integral. The results also exemplified that non-target absorbed-doses such as the liver, spleen and pancreas were approximately 0.008, 0.004, and 0.039, respectively. While these values were so much lower than target (tumor) absorbed-dose, it seems due to this low toxicity, this complex is a good agent for therapy.

Keywords: ¹⁷⁷Lu, breast cancer, compartmental modeling, dosimetry

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Authors: Javier Fernandez, Mayte Medina, Rafael Fernandez de Canete, Nuria Alcain, Juan Carlos Ramos-Diaz

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At present, the experimentation of anesthetic drugs on patients requires a regulation protocol, and the response of each patient to several doses of entry drug must be well known. Therefore, the development of pharmacological dose control systems is a promising field of research in anesthesiology. In this paper, it has been developed a non-linear compartmental the pharmacokinetic-pharmacodynamical model which describes the anesthesia depth effect in a sufficiently reliable way over a set of patients with the depth effect quantified by the Bi-Spectral Index. Afterwards, an Artificial Neural Network (ANN) predictive controller has been designed based on the depth of anesthesia model so as to keep the patient in the optimum condition while he undergoes surgical treatment. For the purpose of quantifying the efficiency of the neural predictive controller, a classical proportional-integral-derivative controller has also been developed to compare both strategies. Results show the superior performance of predictive neural controller during BiSpectral Index reference tracking.

Keywords: anesthesia, bi-spectral index, neural network control, pharmacokinetic-pharmacodynamical model

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Authors: Yichao Liu, Peter Fransson, Julian Heidecke, Jonas Wallin, Joacim Rockloev

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Dengue, a mosquito-borne viral disease, poses a significant public health challenge in endemic tropical or subtropical countries, including Sri Lanka. To reveal insights into the complexity of the dynamics of this disease and study the drivers, a comprehensive model capable of both robust forecasting and insightful inference of drivers while capturing the co-circulating of several virus strains is essential. However, existing studies mostly focus on only one aspect at a time and do not integrate and carry insights across the siloed approach. While mechanistic models are developed to capture immunity dynamics, they are often oversimplified and lack integration of all the diverse drivers of disease transmission. On the other hand, purely data-driven methods lack constraints imposed by immuno-epidemiological processes, making them prone to overfitting and inference bias. This research presents a hybrid model that combines machine learning techniques with mechanistic modelling to overcome the limitations of existing approaches. Leveraging eight years of newly reported dengue case data, along with socioeconomic factors, such as human mobility, weekly climate data from 2011 to 2018, genetic data detecting the introduction and presence of new strains, and estimates of seropositivity for different districts in Sri Lanka, we derive a data-driven vector (SEI) to human (SEIR) model across 16 regions in Sri Lanka at the weekly time scale. By conducting ablation studies, the lag effects allowing delays up to 12 weeks of time-varying climate factors were determined. The model demonstrates superior predictive performance over a pure machine learning approach when considering lead times of 5 and 10 weeks on data withheld from model fitting. It further reveals several interesting interpretable findings of drivers while adjusting for the dynamics and influences of immunity and introduction of a new strain. The study uncovers strong influences of socioeconomic variables: population density, mobility, household income and rural vs. urban population. The study reveals substantial sensitivity to the diurnal temperature range and precipitation, while mean temperature and humidity appear less important in the study location. Additionally, the model indicated sensitivity to vegetation index, both max and average. Predictions on testing data reveal high model accuracy. Overall, this study advances the knowledge of dengue transmission in Sri Lanka and demonstrates the importance of incorporating hybrid modelling techniques to use biologically informed model structures with flexible data-driven estimates of model parameters. The findings show the potential to both inference of drivers in situations of complex disease dynamics and robust forecasting models.

Keywords: compartmental model, climate, dengue, machine learning, social-economic

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Authors: Getachew Tilahun, Oluwole Makinde, David Malonza

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We propose and analyze a non-linear mathematical model for the transmission dynamics of pneumonia disease in a population of varying size. The deterministic compartmental model is studied using stability theory of differential equations. The effective reproduction number is obtained and also the local and global asymptotically stability conditions for the disease free and as well as for the endemic equilibria are established. The model exhibit a backward bifurcation and the sensitivity indices of the basic reproduction number to the key parameters are determined. Using Pontryagin’s maximum principle, the optimal control problem is formulated with three control strategies; namely disease prevention through education, treatment and screening. The cost effectiveness analysis of the adopted control strategies revealed that the combination of prevention and treatment is the most cost effective intervention strategies to combat the pneumonia pandemic. Numerical simulation is performed and pertinent results are displayed graphically.

Keywords: cost effectiveness analysis, optimal control, pneumonia dynamics, stability analysis, numerical simulation

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Authors: Pamela R. Jackson, Andrea Hawkins-Daarud, Cassandra R. Rickertsen, Kamala Clark-Swanson, Scott A. Whitmire, Kristin R. Swanson

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Glioblastoma Multiforme (GBM), the most common primary brain tumor, often presents with hyperintensity on T2-weighted or T2-weighted fluid attenuated inversion recovery (T2/FLAIR) magnetic resonance imaging (MRI). This hyperintensity corresponds with vasogenic edema, however there are likely many infiltrating tumor cells within the hyperintensity as well. While MRIs do not directly indicate tumor cells, MRIs do reflect the microenvironmental water abnormalities caused by the presence of tumor cells and edema. The inherent heterogeneity and resulting MRI features of GBMs complicate assessing disease response. To understand how hyperintensity on T2/FLAIR MRI may correlate with edema in the extracellular space (ECS), a multi-compartmental MRI signal equation which takes into account tissue compartments and their associated volumes with input coming from a mathematical model of glioma growth that incorporates edema formation was explored. The reasonableness of two possible extracellular space schema was evaluated by varying the T2 of the edema compartment and calculating the possible resulting T2s in tumor and peripheral edema. In the mathematical model, gliomas were comprised of vasculature and three tumor cellular phenotypes: normoxic, hypoxic, and necrotic. Edema was characterized as fluid leaking from abnormal tumor vessels. Spatial maps of tumor cell density and edema for virtual tumors were simulated with different rates of proliferation and invasion and various ECS expansion schemes. These spatial maps were then passed into a multi-compartmental MRI signal model for generating simulated T2/FLAIR MR images. Individual compartments’ T2 values in the signal equation were either from literature or estimated and the T2 for edema specifically was varied over a wide range (200 ms – 9200 ms). T2 maps were calculated from simulated images. T2 values based on simulated images were evaluated for regions of interest (ROIs) in normal appearing white matter, tumor, and peripheral edema. The ROI T2 values were compared to T2 values reported in literature. The expanding scheme of extracellular space is had T2 values similar to the literature calculated values. The static scheme of extracellular space had a much lower T2 values and no matter what T2 was associated with edema, the intensities did not come close to literature values. Expanding the extracellular space is necessary to achieve simulated edema intensities commiserate with acquired MRIs.

Keywords: extracellular space, glioblastoma multiforme, magnetic resonance imaging, mathematical modeling

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Authors: Justin-Herve Noubissi, Jean Claude Kamgang, Eric Ramat, Januarius Asongu, Christophe Cambier

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The goal of our study is to analyse the impact of climatic factors in malaria transmission taking into account migration between Douala and Yaoundé, two cities of Cameroon country. We show how variations of climatic factors such as temperature and relative humidity affect the malaria spread. We propose a meta-population model of the dynamic transmission of malaria that evolves in space and time and that takes into account temperature and relative humidity and the migration between Douala and Yaoundé. We also integrate the variation of environmental factors as events also called mathematical impulsion that can disrupt the model evolution at any time. Our modelling has been done using the Discrete EVents System Specification (DEVS) formalism. Our implementation has been done on Virtual Laboratory Environment (VLE) that uses DEVS formalism and abstract simulators for coupling models by integrating the concept of DEVS.

Keywords: compartmental models, DEVS, discrete events, meta-population model, VLE

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Authors: Ofosuhene O. Apenteng, Noor Azina Ismail

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Recently tourism is a major foreign exchange earner in the World. In this paper, we propose the mathematical model to study the impact of tourists on the spread of HIV incidences using compartmental differential equation models. Simulation studies of reproduction number are used to demonstrate new insights on the spread of HIV disease. The periodogram analysis of a time series was used to determine the speed at which the disease is spread. The results indicate that with the persistent flow of tourism into a country, the disease status has increased the epidemic rate. The result suggests that the government must put more control on illegal prostitution, unprotected sexual activity as well as to emphasis on prevention policies that include the safe sexual activity through the campaign by the tourism board.

Keywords: HIV/AIDS, mathematical transmission modeling, tourists, stability, simulation

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Authors: J. Fernandez, R. Fernandez de Canete, J. Perea-Paizal, J. C. Ramos-Diaz

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The high prevalence of cardiovascular diseases has provoked a raising interest in the development of mathematical models in order to evaluate the cardiovascular function both under physiological and pathological conditions. In this paper, a physical model of the cardiovascular system with intrinsic regulation is presented and implemented by using the object-oriented Modelica simulation software tools.  For this task, a multi-compartmental system previously validated with physiological data has been built, based on the interconnection of cardiovascular elements such as resistances, capacitances and pumping among others, by following an electrohydraulic analogy. The results obtained under both physiological and pathological scenarios provide an easy interpretative key to analyze the hemodynamic behavior of the patient. The described approach represents a valuable tool in the teaching of physiology for graduate medical and nursing students among others.

Keywords: cardiovascular system, MODELICA simulation software, physical modelling, teaching tool

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Authors: Abdullah Eqal Al Mazrooei

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In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: Abhishek Agarwal, Manoj Sarda, Juhi Kaushik, Vatsal Sanjay, Arup Kumar Das

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Propagation of fire through a non-air conditioned railway compartment is studied by virtue of numerical simulations. Simultaneous computational fire dynamics equations, such as Navier-Stokes, lumped species continuity, overall mass and energy conservation, and heat transfer are solved using finite volume based (for radiation) and finite difference based (for all other equations) solver, Fire Dynamics Simulator (FDS). A single coupe with an eight berth occupancy is used to establish the numerical model, followed by the selection of a three coupe system as the fundamental unit of the locomotive compartment. Heat Release Rate Per Unit Area (HRRPUA) of the initial fire is varied to consider a wide range of compartmental fires. Parameters, such as air inlet velocity relative to the locomotive at the windows, the level of interaction with the ambiance and closure of middle berth are studied through a wide range of numerical simulations. Almost all the loss of lives and properties due to fire breakout can be attributed to the direct or indirect exposure to flames or to the inhalation of toxic gases and resultant suffocation due to smoke and soot. Therefore, the temporal stature of fire and smoke are reported for each of the considered cases which can be used in the present or extended form to develop guidelines to be followed in case of a fire breakout.

Keywords: fire dynamics, flame propagation, locomotive fire, soot flow pattern, non-air-conditioned coaches

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Authors: Entisar A. Elgmati

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Recurrent infant diarrhea is studied using daily data collected in Salvador, Brazil over one year and three months. A logistic regression model is fitted instead of Aalen's additive model using the same covariates that were used in the analysis with the additive model. The model gives reasonably similar results to that using additive regression model. In addition, the problem with the estimated conditional probabilities not being constrained between zero and one in additive model is solved here. Also martingale residuals that have been used to judge the goodness of fit for the additive model are shown to be useful for judging the goodness of fit of the logistic model.

Keywords: additive model, cumulative probabilities, infant diarrhoea, recurrent event

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Authors: Mechlouch Ridha Fethi

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This paper presents a recent mathematical model in political sciences concerning democracy. The model is represented by a logarithmic equation linking the Relative Index of Democracy (RID) to Participation Ratio (PR). Firstly the meanings of the different parameters of the model were presented; and the variation curve of the RID according to PR with different critical areas was discussed. Secondly, the model was applied to a virtual group where we show that the model can be applied depending on the gender. Thirdly, it was observed that the model can be extended to different language models of democracy and that little use to assess the state of democracy for some International organizations like UNO.

Keywords: democracy, mathematic, modelization, quantification

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Authors: Le Kang

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On the research question of 'how to achieve USR', this contribution reflects the concept of university social responsibility, identify three achievement models of USR as the society - diversified model, the university-cooperation model, the government - compound model, also conduct a case study to explore characteristics of Chinese achievement model of USR. The contribution concludes with discussion of how the university, government and society balance demands and roles, make necessarily strategic adjustment and innovative approach to repair the shortcomings of each achievement model.

Keywords: modern university, USR, achievement model, compound model

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Authors: Zhou Jianhong

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Model averaging is a desirable approach to deal with model uncertainty, which, however, has rarely been explored for Poisson regression. In this paper, we propose a model averaging procedure based on an unbiased estimator of the expected Kullback-Leibler distance for the Poisson regression. Simulation study shows that the proposed model average estimator outperforms some other commonly used model selection and model average estimators in some situations. Our proposed methods are further applied to a real data example and the advantage of this method is demonstrated again.

Keywords: model averaging, poission regression, Kullback-Leibler distance, statistics

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Authors: L. Madouni, M. Ould Ouali, N. E. Hannachi

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Two constitutive models for concrete are available in ABAQUS/Explicit, the Brittle Cracking Model and the Concrete Damaged Plasticity Model, and their suitability and limitations are well known. The aim of the present paper is to implement a damage-friction concrete constitutive model and to evaluate the performance of this model by comparing the predicted response with experimental data. The constitutive formulation of this material model is reviewed. In order to have consistent results, the parameter identification and calibration for the model have been performed. Several numerical simulations are presented in this paper, whose results allow for validating the capability of the proposed model for reproducing the typical nonlinear performances of concrete structures under different monotonic and cyclic load conditions. The results of the evaluation will be used for recommendations concerning the application and further improvements of the investigated model.

Keywords: Abaqus, concrete, constitutive model, numerical simulation

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