The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

This paper considers the outcome of a formal sensitivity analysis on a series of epidemic model structures developed to study the population level effects of maternal antibodies. The analysis is used to compare the potential influence of maternally acquired immunity on various age and time domain observations of infection and serology, with and without seasonality. The results of the analysis indicate that time series observations are largely insensitive to variations in the average duration of this protection, and that age related empirical data are likely to be most appropriate for estimating these characteristics

A multispecies model for the transmission and control of mastitis in dairy cows

Mastitis in dairy cows is a significant economic and animal welfare issue in the dairy industry. The bacterial pathogens responsible for infection of the mammary gland may be split into two main categories: major and minor pathogens. Infection with major pathogens generally results in clinical illness or strong inflammatory responses and reduced milk yields, whereas minor pathogen infection is usually subclinical. Previous investigations have considered the transmission of these pathogens independently. Experimental evidence has shown cross-protection between species of pathogens. In this study a mathematical model for the coupled transmission of major and minor pathogens along with their interaction via the host was developed in order to consider various methods for controlling the incidence of major pathogen infection. A stability analysis of the model equilibria provides explanations for observed phenomena and previous decoupled modelling results. This multispecies model structure has provided a basis for quantifying the extent of cross-protection between species and assessing possible control strategies against the disease

Modelling the dynamics of intramammary E. coli infections in dairy cows: understanding mechanisms that distinguish transient from persistent infections

The majority of intramammary infections with Escherichia coli in dairy cows result in transient infections with duration of about 10 days or less, although more persistent infections (2 months or longer) have been identified. We apply a mathematical model to explore the role of an intracellular mammary epithelial cell reservoir in the dynamics of infection. We included biological knowledge of the bovine immune response and known characteristics of the bacterial population in both transient and persistent infections. The results indicate that varying the survival duration of the intracellular reservoir reproduces the data for both transient and persistent infections. Survival in an intracellular reservoir is the most likely mechanism that ensures persistence of E. coli infections in mammary glands. Knowledge of the pathogenesis of persistent infections is essential to develop preventive and treatment programmes for these important infections in dairy cows

A coupled drug kinetics-cell cycle model to analyse the response of human cells to intervention by topotecan

A model describing the response of the growth of single human cells in the absence and presence of the anti-cancer agent topotecan (TPT) is presented. The model includes a novel coupling of both the kinetics of TPT and cell cycle responses to the agent. By linking the models in this way, rather than using separate (disjoint) approaches, it is possible to illustrate how the drug perturbs the cell cycle. The model is compared to experimental in vitro cell cycle response data (comprising single cell descriptors for molecular and behavioural events), showing good qualitative agreement for a range of TPT dose levels

Lyapunov exponents for certain stochastic flows

This thesis examines the asymptotic behaviour of solution flows of certain stochastic differential equations utilising the theory of Lyapunov exponents. The approach is taken on two fronts. Initially flows are considered on compact manifolds that arise from embedding the manifold in some Euclidean space - the Gradient Brownian flow. In this case the existence of the Lyapunov exponents is known. Results are obtained for the sum of the exponents - which has the geometrical interpretation as the exponential rate of change of volume under the action of the flow - and for the largest exponent on generalised Clifford Tori and convex hypersurfaces. The situation on non-compact manifolds is then considered - where the existence of the exponents is uncertain due to the fact that the existence of a finite invariant measure is not guaranteed. However, by considering a stochastic mechanical system this problem is overcome and conditions for existence are obtained for both the Lyapunov spectrum and the sum' of the exponents. Some examples are then considered in the noncompact case. Finally in the Appendix a computational method for calculating the largest Lyapunov exponent on a hypersurface is considered

Kinerja Pengawas SMA/SMK Ditinjau dari Lingkungan Kerja dan Motivasi Kerja di Wilayah Kaili

Tujuan penelitian ini adalah untuk mengetahui besar hubungan kinerja pengawas SMA/SMK di tinjau dari lingkungan kerja dan motivasi kerja pengawas sekolah di Wilayah Kaili. (1) Lingkungan kerja dengan kinerja pengawas SMA/SMK di Wilayah Kaili, (2) Motivasi kerja dengan kinerja pengawas SMA/SMK di Wilayah Kaili, (3) Lingkungan kerja dan motivasi kerja dengan Kinerja pengawas SMA/SMK di Wilayah Kaili, (4) Lingkungan kerja dengan kinerja pengawas SMA/SMK di Wilayah Kaili apabila motivasi kerja dikontrol, (5) Motivasi kerja dengan kinerja pengawas SMA/SMK di Wilayah Kaili apabila lingkungan kerja pengawas dikontrol. Penelitian ini adalah penelitian survey yang bersifat korelasional. Populasi dalam penelitian ini adalah seluruh pengawas SMA / SMK di Wilayah Kaili yaitu Kota Palu, Kabupaten Donggala, Kabupaten Parigi, dan Kabupaten Sigi dengan jumlah pengawas sekolah 48 orang. Pengambilan sampel dilakukan secara rambang sederhana. Ukuran sampel dalam penelitian ini sebanyak 43 pengawas sekolah sebagai responden. Mengidentifikasi data sebagai outlier dari sekumpulan data yang menyimpang, terdapat 7 data pencilan sehingga data yang diinferensi sebanyak 37 orang. Instrumen yang digunakan berupa kuesioner. Pengembangan instrumen dilakukan mulai dari menyusun indikator, kisi-kisi instrumen, kemudian butir-butir instrumen yang di validasi isi, analisis butir secara kualitatif sehingga instrumen siap digunakan. Data dianalisis dengan menggunakan analisis deskriptif dan analisis inferensial. Hasil analisis deskriptif menunjukkan bahwa lingkungan kerja, motivasi kerja dan kinerja pengawas sekolah berada pada kategori baik. Hasil analisis inferensial menunjukkan bahwa: (1) Lingkungan kerja tidak mempunyai hubungan yang positif dan signifikan dengan kinerja pengawas SMA/SMK, (2) Motivasi kerja mempunyai hubungan yang positif dan signifikan dengan kinerja pengawas SMA/SMK, (3) Lingkungan kerja dan motivasi kerja mempunyai hubungan yang positif dan signifikan dengan Kinerja pengawas SMA/SMK, (4) Lingkungan kerja tidak mempunyai hubungan yang positif dan signifikan dengan kinerja pengawas SMA/SMK apabila motivasi kerja dikontrol, (5) Motivasi kerja mempunyai hubungan yang positif dan signifikan dengan kinerja pengawas SMA/SMK apabila lingkungan kerja pengawas dikontrol

Input-dependent structural identifiability of nonlinear systems

A dynamic model is structurally identifiable if it is possible to infer its unknown parameters by observing its output. Structural identifiability depends on the system dynamics, output, and input, as well as on the specific values of initial conditions and parameters. Here we present a symbolic method that characterizes the input that a model requires to be structurally identifiable. It determines which derivatives must be non-zero in order to have a sufficiently exciting input. Our approach considers structural identifiability as a generalization of nonlinear observability and incorporates extended Lie derivatives. The methodology assesses structural identifiability for time-varying inputs and, additionally, it can be used to determine the input profile that is required to make the parameters structurally locally identifiable. Furthermore, it is sometimes possible to replace an experiment with time-varying input with multiple experiments with constant inputs. We implement the resulting method as a MATLAB toolbox named STRIKE-GOLDD2. This tool can assist in the design of new experiments for the purpose of parameter estimation

A mathematical model characterising Achilles tendon dynamics in flexion

The purpose of this study is to acquire mechanistic knowledge of the gastrocnemius muscle-Achilles tendon complex behaviour during specific movements in humans through mathematical modelling. Analysis of this muscle-tendon complex was performed to see if already existing muscle-tendon models of other parts of the body could be applied to the leg muscles, especially the gastrocnemius muscle-Achilles tendon complex, and whether they could adequately characterise its behaviour. Five healthy volunteers were asked to take part in experiments where dorsiflexion and plantar flexion of the foot were studied. A model of the Achilles tendon-gastrocnemius muscle was developed, incorporating assumptions regarding the mechanical properties of the muscle fibres and the tendinous tissue in series. Ultrasound images of the volunteers, direct measurements and additional mathematical calculations were used to parameterise the model. Ground reaction forces, forces on specific joints and moments and angles for the ankle were obtained from a Vicon 3D motion capture system. Model validation was performed from the experimental data captured for each volunteer and from reconstruction of the movements of specific trajectories of the joints, muscles and tendons involved in those movements

Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches

Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery

Systems pharmacology approach for prediction of pulmonary and systemic pharmacokinetics and receptor occupancy of inhaled drugs

Pulmonary drug disposition after inhalation is complex involving mechanisms, such as regional drug deposition, dissolution, and mucociliary clearance. This study aimed to develop a systems pharmacology approach to mechanistically describe lung disposition in rats and thereby provide an integrated understanding of the system. When drug- and formulation-specific properties for the poorly soluble drug fluticasone propionate were fed into the model, it proved predictive of the pharmacokinetics and receptor occupancy after intravenous administration and nose-only inhalation. As the model clearly distinguishes among drug-specific, formulation-specific, and system-specific properties, it was possible to identify key determinants of pulmonary selectivity of receptor occupancy of inhaled drugs: slow particle dissolution and slow drug-receptor dissociation. Hence, it enables assessment of factors for lung targeting, including molecular properties, formulation, as well as the physiology of the animal species, thereby providing a general framework for rational drug design and facilitated translation of lung targeting from animal to man