Bayesian inference of a dynamical model evaluating Deltamethrin effect on Daphnia survival

The estimation of toxicokinetic and toxicodynamic (TK-TD) models parameters is a real problem in research. These models highlight a dynamics of internalisation of a toxic compound and a dynamics of the damage that this contaminant will cause on an organism and of possible repairs on the latter. This coupling TK-TD makes it possible to connect these measurements at different times with the same set of parameters sometimes very important in number. In this paper, the focus is on assessing the long-term impact of deltamethrin effects on a sample of daphnia magna survival. For this purpose we fit our TK-TD model of deltamethrin bio-accumuluation and daphnia survival to our experimental data by using bayesian inference algorithm developed in the package deBinfer of R. This bayesian inference method allows estimate simultaneously all the parameters of deltamethrin bio-accumuluation and daphnia survival dynamical system. For the estimation of the environmental risks, our results show that whatever the concentration or duration of exposure, the concentration of bioaccumulated deltamerin should not exceed on average 6.188 ng/L, at the risk of observing the deadly effects

A stochastic model for active transport

We develop a stochastic model for an intracellular active transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (mean first passage time). We study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition) and the presence of obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular transport (which can result, for example, in several neurological disorders. From a mathematical point of view, the intracellular active transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.

Foreword to BIOMATH 2017 Proceedings: Some comments on mathematical modelling and biomathematics.

Both biology and mathematics have existed as well established branches of science for hundreds of years and both, maybe not in a well defined way, have been with the humankind for a couple of thousands of years. Though nature was studied by the ancient civilizations of Mesopotamia, Egypt, the Indian subcontinent and China, the origins of modern biology are typically traced back to the ancient Greece, where Aristotle (384-322 BC) contributed most extensively to its development. Similarly, the ancient Babylonians were able to solve quadratic equation over four millennia ago and we can see the development of mathematical methods in all ancient civilisations, notably in China and on the Indian subcontinent. However, possibly again the Greeks were the first who studied mathematics for its own sake, as a collection of abstract objects and relations between them. Nevertheless, despite the fact that the development of such a mathematics has not required any external stimuli, an amazing feature of the human mind is that a large number of abstract mathematical constructs has proved to be very well suited for describing natural phenomena.This prompted Eugene Wigner to write his famous article The Unreasonable Effectiveness of Mathematics in the Natural Sciences, ...

Sensitivity analysis for a within-human-host immuno-pathogenesis dynamics of Plasmodium falciparum parasites

Sensitivity analysis has become increasingly useful in many fields of engineering and sciences. Researchers use sensitivity and uncertainty analysis in the mathematical modelling of biological phenomena because of its value in identifying essential parameters for model's output. Moreover, it can help in the process of experimental analysis, model order reduction, parameter estimation, decision making or development of recommendations for decision makers. Here, we demonstrate the use of local sensitivity analysis to understand the influence of different parameters on a threshold parameter, R_0^I, resulting from the analysis of a within human-host model for the dynamics of malaria parasites. %We highlight the different methods used in sensitivity analysis.Our results reveal that the obtained R_0^I is most sensitive to the infection rate of healthy red blood cells (RBCs) by merozoites, the average number of merozoites released per bursting parasitized RBCs, the proportion of parasitized RBCs that continue asexual reproduction and the per capita natural death rate of merozoites.

Numerical solutions of a 2D fluid problem coupled to a nonlinear non-local reaction-advection-diffusion problem for cell crawling migration in a discoidal domain

In this work, we present a numerical scheme for the approximate solutions of a 2D crawling cell migration problem. The model, defined on a non-deformable discoidal domain, consists in a Darcy fluid problem coupled with a Poisson problem and a reaction-advection-diffusion problem. Moreover, the advection velocity depends on boundary values, making the problem nonlinear and non local. For a discoidal domain, numerical solutions can be obtained using the finite volume method on the polar formulation of the model. Simulations show that different migration behaviours can be captured.

Estimating the mean of a small sample under the two parameter lognormal distribution

Lognormally distributed variables are found in biological, economic and other systems. Here the sampling distributions of maximum likelihood estimates (MLE) for parameters are developed when data are lognormally distributed and estimation is carried out either by the correct lognormal model or by the mis-specified normal distribution. This is designed as an aid to experimental design when drawing a small sample under an assumption that the population follows a normal distribution while in fact it follows a lognormal distribution. Distributions are derived analytically as far as possible by using a technique for estimator densities and are confirmed by simulations. For an independently and identically distributed lognormal sample, when a normal distribution is used for estimation then the distribution of the MLE of the mean is different to that for the MLE of the lognormal mean. The distribution is not known but can be well enough approximated by another lognormal. An analytic method for the distribution of the mis-specified normal variance uses computational convolution for a sample of size 2. The expected value of the mis-specified normal variance is also found as a way to give information about the effect of the model misspecification on inferences for the mean. The results are demonstrated on an example for a population distribution that is abstracted from a survey.

Analysis of model for the transmission dynamics of Zika with sterile insect technique

A deterministic model for the transmission dynamics of Zika, that takes into account the aquatic and non-aquatic stages of mosquito development is constructed and rigorously analysed. The model with fraction of male mosquitoes being sterilized assumed direct (human-human) and indirect (human-mosquito-human) transmission. Stability analysis of the equilibria and sensitivity analysis of parameters associated with the computed reproduction number were presented. Numerical simulation were carried out to support the analysis.

Analysis of a mathematical model of the dynamics of contagious bovine pleuropneumonia

Contagious bovine pleuropneumonia (CBPP) is a disease of cattle and water buffalo caused by Mycoplasma mycoides subspecies mycoides (Mmm). It attacks the lungs and the membranes that line the thoracic cavity. The disease is transmitted by inhaling droplets disseminated through coughing by infected cattle. In this paper a deterministic mathematical model for the transmission of Contagious Bovine plueropnemonia is presented. The model is a five compartmental model consisting of susceptible, Exposed, Infectious, Persistently infected and Recovered compartments. We derived a formula for the basic reproduction number R0. For R0 ≤ 1, the disease free equilibrium is globally asymptotically stable, thus CBPP dies out; whereas for R0 > 1, the unique endemic equilibrium is globally asymptotically stable and hence the disease persists. Elasticity indices for R0 with respect to different parameters are calculated; indicating parameters that are important for control strategies to bring R0 below 1, the effective contact rate β has the largest elasticity index. As the disease control options are associated to these parameters, for some values of these parameters, R0 < 1, thus the disease can be controlled.

Modelling of activator-inhibitor dynamics via nonlocal integral operators

This paper proposes application of nonlocal operators to represent the biological pattern formation mechanism of self-activation and lateral inhibition. The blue-green algae Anabaena is discussed as a model example. The patterns are determined by the kernels of the integrals representing the nonlocal operators. The emergence of patters when varying the size of the support of the kernels is numerically investigated.

Stability analysis of a compartmental SEIHRD model for the Ebola virus disease

In this work, we perform a stability analysis of a compartmental SEIHRD model. This model is a simplified version of a previous approach. In this previous work, we proposed an original deterministic spatial-temporal model, called Be-CoDiS (Between-Countries Disease Spread), to study the evolution of human diseases within and between countries. This model was validated by considering data from the 2014-16 West African Ebola Virus Disease epidemic. Here, considering some simplification assumptions in Be-CODIS, our goal is to study the equilibria of the model and their stability using the basic reproduction ratio as a threshold parameter. Finally, we validate the obtained results by considering some numerical experiments based on data from the 2014-16 West African Ebola Virus Disease epidemic.