Maximal reproduction number estimation and identification of transmission rate from the first inflection point of new infectious cases waves: COVID-19 outbreak example.

The dynamics of COVID-19 pandemic varies across countries and it is important for​ researchers to study different kind of phenomena observed at different stages of the waves during the epidemic period. Our interest in this paper is not to model what happened during the endemic state but during the epidemic state. We proposed a continuous formulation of a unique maximum reproduction number estimate with an assumption that the epidemic curve is in form of the Gaussian curve and then compare the model with the discrete form and the observed basic reproduction number during the contagiousness period considered. Furthermore, we estimated the transmission rate from identification of the first inflection point of a wave of the curve of daily new infectious cases using the Bernoulli S-I (Susceptible-Infected) equation. We applied this new method to the real data from Cameroon COVID-19 outbreak both at national and regional levels. High correlation was observed between the socio-economic parameters and epidemiology parameters at regional level in Cameroon. Also, the method was applied to the second wave COVID-19 outbreak for the world data which is a period the phenomena we are considering were observed. Lastly, it was observed that the models presented results correspond with the epidemic dynamics in Cameroon and World data. We recommend that it is important to study what happened during the growth inflection point as some countries data did not climax.

SI epidemic model applied to COVID-19 data in mainland China.

The article is devoted to the parameters identification in the SI model. We consider several methods, starting with an exponential fit to the early cumulative data of SARS-CoV2 in mainland China. The present methodology provides a way to compute the parameters at the early stage of the epidemic. Next, we establish an identifiability result. Then we use the Bernoulli-Verhulst model as a phenomenological model to fit the data and derive some results on the parameters identification. The last part of the paper is devoted to some numerical algorithms to fit a daily piecewise constant rate of transmission.

Reduction of Prolonged Excessive Pressure in Seated Persons With Paraplegia Using Wireless Lingual Tactile Feedback: A Randomized Controlled Trial.

Pressure ulcers (PU) are known to be a high-cost disease with a risk of severe morbidity. This paper evaluates a new clinical strategy based on an innovative medical device [Tongue Display Unit (TDU)] that implements perceptive supplementation in order to reduce prolonged excessive pressure, recognized as one of the main causes of PU. A randomized, controlled, and parallel-group trial was carried out with 12 subjects with spinal cord injuries (SCI). Subjects were assigned to the control (without TDU, [Formula: see text]) or intervention (with TDU, [Formula: see text]) group. Each subject took part in two sessions, during which the subject, seated on a pressure map sensor, watched a movie for one hour. The TDU was activated during the second session of the intervention group. Intention-to-treat analysis showed that the improvement in adequate weight shifting between the two sessions was higher in the intervention group (0.84 [0.24; 0.89]) than in the control group (0.01 [-0.01; 0.09]; [Formula: see text]) and that the ratio of prolonged excessive pressure between the two sessions was lower in the intervention group (0.74 [0.37; 1.92]) than in the control group (1.72 [1.32; 2.56]; [Formula: see text]). The pressure map sensor was evaluated as being convenient for use in daily life; however, this was not the case for the TDU. This paper shows that persons with SCI could benefit from a system based on perceptive supplementation that alerts and guides the user on how to adapt their posture in order to reduce prolonged excessive pressure, one of the main causes of PU.

Estimation of life expectancy of patients diagnosed with the most common cancers in the Valparaiso Region, Chile.

BACKGROUND: The 1000s of people who die from cancer each year have become one of the leading causes of death among the Chilean population, placing it as the second cause of death in the region of Valparaiso between 1997 and 2003. Statistics have provided different measures regarding the life expectancy of cancer patients which have resulted in being useful to establish courses of action for prevention and treatment plans to follow. METHODS: Data was extracted from the cancer module of the Epidemiology Assistance System (SADEPI for its initials in Spanish) which stores information about cancer cases in the provinces of Valparaiso and Petorca. The survival period is defined as the difference in days between the date of occurrence and the date of death of the patient by separating the data into quartiles. RESULTS: The more frequent cancers in the region of Valparaiso behave similarly to global behaviours of the disease. The majority of affected patients are around 65 years of age which progressively lowers its occurrence in younger adults under the age of 45. CONCLUSIONS: Further efforts are required for early detection and timely access to treatment for cancer patients. Statistics are an important support in achieving this.

Discrete Mesh Approach in Morphogenesis Modelling: the Example of Gastrulation.

Morphogenesis is a general concept in biology including all the processes which generate tissue shapes and cellular organizations in a living organism. Many hybrid formalizations (i.e., with both discrete and continuous parts) have been proposed for modelling morphogenesis in embryonic or adult animals, like gastrulation. We propose first to study the ventral furrow invagination as the initial step of gastrulation, early stage of embryogenesis. We focus on the study of the connection between the apical constriction of the ventral cells and the initiation of the invagination. For that, we have created a 3D biomechanical model of the embryo of the Drosophila melanogaster based on the finite element method. Each cell is modelled by an elastic hexahedron contour and is firmly attached to its neighbouring cells. A uniform initial distribution of elastic and contractile forces is applied to cells along the model. Numerical simulations show that invagination starts at ventral curved extremities of the embryo and then propagates to the ventral medial layer. Then, this observation already made in some experiments can be attributed uniquely to the specific shape of the embryo and we provide mechanical evidence to support it. Results of the simulations of the "pill-shaped" geometry of the Drosophila melanogaster embryo are compared with those of a spherical geometry corresponding to the Xenopus lævis embryo. Eventually, we propose to study the influence of cell proliferation on the end of the process of invagination represented by the closure of the ventral furrow.

Wound Healing and Scale Modelling in Zebrafish.

We propose to study the wound healing in Zebrafish by using firstly a differential approach for modelling morphogens diffusion and cell chemotactic motion, and secondly a hybrid model of tissue regeneration, where cells are considered as individual objects and molecular concentrations are described by partial differential equations.

The Poitiers School of Mathematical and Theoretical Biology: Besson-Gavaudan-Schützenberger's Conjectures on Genetic Code and RNA Structures.

The French school of theoretical biology has been mainly initiated in Poitiers during the sixties by scientists like J. Besson, G. Bouligand, P. Gavaudan, M. P. Schützenberger and R. Thom, launching many new research domains on the fractal dimension, the combinatorial properties of the genetic code and related amino-acids as well as on the genetic regulation of the biological processes. Presently, the biological science knows that RNA molecules are often involved in the regulation of complex genetic networks as effectors, e.g., activators (small RNAs as transcription factors), inhibitors (micro-RNAs) or hybrids (circular RNAs). Examples of such networks will be given showing that (1) there exist RNA "relics" that have played an important role during evolution and have survived in many genomes, whose probability distribution of their sub-sequences is quantified by the Shannon entropy, and (2) the robustness of the dynamics of the networks they regulate can be characterized by the Kolmogorov-Sinaï dynamic entropy and attractor entropy.

Discrete dynamics of contagious social diseases: Example of obesity.

Modeling contagious diseases needs to incorporate information about social networks through which the disease spreads as well as data about demographic and genetic changes in the susceptible population. In this paper, we propose a theoretical framework (conceptualization and formalization) which seeks to model obesity as a process of transformation of one's own body determined by individual (physical and psychological), inter-individual (relational, i.e., relative to the relationship between the individual and others) and socio-cultural (environmental, i.e., relative to the relationship between the individual and his milieu) factors. Individual and inter-individual factors are tied to each other in a socio-cultural context whose impact is notably related to the visibility of anybody being exposed on the public stage in a non-contingent way. The question we are dealing with in this article is whether such kind of social diseases, i.e., depending upon socio-environmental exposure, can be considered as "contagious". In other words, can obesity be propagated from individual to individual or from environmental sources throughout an entire population?

Stability, complexity and robustness in population dynamics.

The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription factors. The networks made of these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks.

Evaluation of a Smartphone-based audio-biofeedback system for improving balance in older adults--a pilot study.

This study was designed to assess the effectiveness of a Smartphone-based audio-biofeedback (ABF) system for improving balance in older adults. This so-called "iBalance-ABF" system that we recetly developed is "all-inclusive" in the sense that its three main components of a balance prosthesis, (i) the sensory input unit, (ii) the processing unit, and (iii) the sensory output unit, are entirely embedded into the Smartphone. The underlying principle of this system is to supply the user with supplementary information about the medial-lateral (ML) trunk tilt relative to a predetermined adjustable "dead zone" through sound generation in earphones. Six healthy older adults voluntarily participated in this pilot study. Eyes closed, they were asked to stand upright and to sway as little as possible in two (parallel and tandem) stance conditions executed without and with the use of the iBalance-ABF system. Results showed that, without any visual information, the use of the Smartphone-based ABF allowed the older healthy adults to significantly decrease their ML trunk sway in the tandem stance posture and to mitigate the destabilizing effect induced by this particular stance. Although an extended study including a larger number of participants is needed to confirm these data, the present results are encouraging. They do suggest that Smartphone-based ABF system could be used for balance training and rehabilitation therapy in older adults.

MitomiRs, chloromiRs and modelling of the microRNA inhibition.

MicroRNAs are non-coding parts of nuclear and mitochondrial genomes, preventing the weakest part of the genetic regulatory networks from being expressed and preventing the appearance of a too many attractors in these networks. They have also a great influence on the chromatin clock, which ensures the updating of the genetic regulatory networks. The post-transcriptional inhibitory activity by the microRNAs, which is partly unspecific, is due firstly to their possibly direct negative action during translation by hybridizing tRNAs, especially those inside the mitochondrion, hence slowing mitochondrial respiration, and secondly to their action on a large number of putative m-RNA targets like those involved in immunetworks; We show that the circuits in the core of the interaction graphs are responsible for the small number of dedicated attractors that correspond to genetically controlled functions, partly due to a general filtering by the microRNAs. We analyze this influence as well as their impact on important functions like the control by the p53 network over the apoptosis/proliferation system and the homeostasis of the energy metabolism. In this last case, we show the role of two kinds of microRNAs, both involved in the control of the mitochondrial genome: (1) nuclear microRNAs, called mitoMirs, inhibiting mitochondrial genes and (2) putative mitochondrial microRNAs inhibiting the tRNAs functioning.

MitomiRs delineating the intracellular localization of microRNAs at mitochondria.

Mitochondria play a crucial role in energetic metabolism, signaling pathways, and overall cell viability. Mitochondrial dysfunctions are known to cause a wide range of human diseases that affect tissues especially those with high energetic requirements, such as skeletal muscle, heart, kidney, and central nervous system, while being involved in cancer, aging, and metabolic processes. At the same time, the microRNA (miRNA) gene family has been demonstrated to be involved in most cellular processes through modulation of proteins critical for cellular homeostasis. Given the broad scope of reactivity profiles and the ability of miRNAs to modify numerous proteomic and genomic processes, new emphasis is being placed on the influence of miRNAs at the mitochondrial level. Recently, the localization of miRNAs in mitochondria was characterized in different species. This raises the idea that those miRNAs, noted "mitomiRs," could act as "vectors" that sense and respond dynamically to the changing microenvironment of mitochondria at the cellular level. Reciprocally, we present the involvement of mitochondria in small RNA biogenesis. With the aim of deciphering the significance of this localization, we discuss the putative mechanism of import of miRNAs at mitochondria, their origin, and their hypothetical roles within the organelle.

Random modelling of contagious diseases.

Modelling contagious diseases needs to include a mechanistic knowledge about contacts between hosts and pathogens as specific as possible, e.g., by incorporating in the model information about social networks through which the disease spreads. The unknown part concerning the contact mechanism can be modelled using a stochastic approach. For that purpose, we revisit SIR models by introducing first a microscopic stochastic version of the contacts between individuals of different populations (namely Susceptible, Infective and Recovering), then by adding a random perturbation in the vicinity of the endemic fixed point of the SIR model and eventually by introducing the definition of various types of random social networks. We propose as example of application to contagious diseases the HIV, and we show that a micro-simulation of individual based modelling (IBM) type can reproduce the current stable incidence of the HIV epidemic in a population of HIV-positive men having sex with men (MSM).

On the number of different dynamics in Boolean networks with deterministic update schedules.

Deterministic Boolean networks are a type of discrete dynamical systems widely used in the modeling of genetic networks. The dynamics of such systems is characterized by the local activation functions and the update schedule, i.e., the order in which the nodes are updated. In this paper, we address the problem of knowing the different dynamics of a Boolean network when the update schedule is changed. We begin by proving that the problem of the existence of a pair of update schedules with different dynamics is NP-complete. However, we show that certain structural properties of the interaction diagraph are sufficient for guaranteeing distinct dynamics of a network. In [1] the authors define equivalence classes which have the property that all the update schedules of a given class yield the same dynamics. In order to determine the dynamics associated to a network, we develop an algorithm to efficiently enumerate the above equivalence classes by selecting a representative update schedule for each class with a minimum number of blocks. Finally, we run this algorithm on the well known Arabidopsis thaliana network to determine the full spectrum of its different dynamics.

iBalance-ABF: a smartphone-based audio-biofeedback balance system.

This paper proposes an implementation of a Kalman filter, using inertial sensors of a smartphone, to estimate 3-D angulation of the trunk. The developed system monitors the trunk angular evolution during bipedal stance and helps the user to improve balance through a configurable and integrated auditory-biofeedback (ABF) loop. A proof-of-concept study was performed to assess the effectiveness of this so-called iBalance-ABF--smartphone-based audio-biofeedback system--in improving balance during bipedal standing. Results showed that young healthy individuals were able to efficiently use ABF on sagittal trunk tilt to improve their balance in the medial-lateral direction. These findings suggest that the iBalance-ABF system as a telerehabilitation system could represent a suitable solution for ambient assisted living technologies.

Predictive power of "a minima" models in biology.

Many apparently complex mechanisms in biology, especially in embryology and molecular biology, can be explained easily by reasoning at the level of the "efficient cause" of the observed phenomenology: the mechanism can then be explained by a simple geometrical argument or a variational principle, leading to the solution of an optimization problem, for example, via the co-existence of a minimization and a maximization problem (a min-max principle). Passing from a microscopic (or cellular) level (optimal min-max solution of the simple mechanistic system) to the macroscopic level often involves an averaging effect (linked to the repetition of a large number of such microscopic systems with possible random choice of the parameters of each of them) that gives birth to a global functional feature (e.g. at the tissue level). We will illustrate these general principles by building in four different domains of application "a minima" models and showing the main properties of their solutions: (1) extraction of a minimal RNA structure functioning as the first "peptidic machine," a kind of ancestral ribosome; (2) study of a genetic regulatory network of Drosophila centred on Engrailed gene and expressing successively two genes inside a limit cycle; (3) study of a genetic network regulating neural activity and proliferation in mammals; and (4) study of a simple geometric model of epiboly in zebrafish.

Can an electro-tactile vestibular substitution system improve balance in patients with unilateral vestibular loss under altered somatosensory conditions from the foot and ankle?

This pilot study aimed at assessing the feasibility and the effectiveness of an electro Electro-tactile Vestibular Substitution System (EVSS) in patients with unilateral vestibular loss under normal and altered somatosensory conditions from the foot and ankle. Four unilateral vestibular-defective patients voluntarily participated in the experiment. They were asked to stand upright as still as possible with their eyes closed in two Normal and Altered foot and ankle sensory conditions. In the Normal condition, the postural task was executed on a firm support surface constituted by the force platform. In the Altered condition, a 2-cm thick foam support surface was placed under the participants' feet. These two foot and ankle sensory conditions were executed under two No EVSS and EVSS experimental conditions. The No EVSS condition served as a control condition. In the EVSS condition, participants executed the postural task using a biofeedback system whose underlying principle consisted of supplying them with additional information about their head orientation/motion with respect to gravitational vertical through electro-tactile stimulation of their tongue. Centre of foot pressure displacements (CoP) were recorded using the force platform. Results showed that, relative to the No EVSS condition, the EVSS condition decreased CoP displacements in both the Normal and the Altered foot and ankle sensory conditions. Interestingly, the stabilizing effect was more pronounced in the Altered than in the Normal foot and ankle sensory condition. These preliminary results suggest that patients with unilateral vestibular loss were able to take advantage to a head position-based electro-tactile tongue biofeedback to mitigate the postural perturbation induced by alteration of somatosensory input from the foot and the ankle.

Demography and diffusion in epidemics: malaria and black death spread.

The classical models of epidemics dynamics by Ross and McKendrick have to be revisited in order to incorporate elements coming from the demography (fecundity, mortality and migration) both of host and vector populations and from the diffusion and mutation of infectious agents. The classical approach is indeed dealing with populations supposed to be constant during the epidemic wave, but the presently observed pandemics show duration of their spread during years imposing to take into account the host and vector population changes as well as the transient or permanent migration and diffusion of hosts (susceptible or infected), as well as vectors and infectious agents. Two examples are presented, one concerning the malaria in Mali and the other the plague at the middle-age.

Can a plantar pressure-based tongue-placed electrotactile biofeedback improve postural control under altered vestibular and neck proprioceptive conditions?

We investigated the effects of a plantar pressure-based tongue-placed electrotactile biofeedback on postural control during quiet standing under normal and altered vestibular and neck proprioceptive conditions. To achieve this goal, 14 young healthy adults were asked to stand upright as immobile as possible with their eyes closed in two Neutral and Extended head postures and two conditions of No-biofeedback and Biofeedback. The underlying principle of the biofeedback consisted of providing supplementary information related to foot sole pressure distribution through a wireless embedded tongue-placed tactile output device. Center of foot pressure (CoP) displacements were recorded using a plantar pressure data acquisition system. Results showed that (1) the Extended head posture yielded increased CoP displacements relative to the Neutral head posture in the No-biofeedback condition, with a greater effect along the anteroposterior than mediolateral axis, whereas (2) no significant difference between the two Neutral and Extended head postures was observed in the Biofeedback condition. The present findings suggested that the availability of the plantar pressure-based tongue-placed electrotactile biofeedback allowed the subjects to suppress the destabilizing effect induced by the disruption of vestibular and neck proprioceptive inputs associated with the head extended posture. These results are discussed according to the sensory re-weighting hypothesis, whereby the CNS would dynamically and selectively adjust the relative contributions of sensory inputs (i.e. the sensory weights) to maintain upright stance depending on the sensory contexts and the neuromuscular constraints acting on the subject.

Pressure sensor-based tongue-placed electrotactile biofeedback for balance improvement--biomedical application to prevent pressure sores formation and falls.

We introduce the innovative technologies, based on the concept of "sensory substitution", we are developing in the fields of biomedical engineering and human disability. Precisely, our goal is to design, develop and validate practical assistive biomedical and/or technical devices and/or rehabilitating procedures for persons with disabilities, using artificial tongue-placed tactile biofeedback systems. Proposed applications are dealing with: (1) pressure sores prevention in case of spinal cord injuries (persons with paraplegia, or tetraplegia); and (2) balance control improvement to prevent fall in older and/or disabled adults. This paper describes the architecture and the functioning principle of these biofeedback systems and presents preliminary results of two feasibility studies performed on young healthy adults.