Dynamically adjusted cell fate decisions and resilience to mutant invasion during steady-state hematopoiesis revealed by an experimentally parameterized mathematical model.

A major next step in hematopoietic stem cell (HSC) biology is to enhance our quantitative understanding of cellular and evolutionary dynamics involved in undisturbed hematopoiesis. Mathematical models have been and continue to be key in this respect, and are most powerful when parameterized experimentally and containing sufficient biological complexity. In this paper, we use data from label propagation experiments in mice to parameterize a mathematical model of hematopoiesis that includes homeostatic control mechanisms as well as clonal evolution. We find that nonlinear feedback control can drastically change the interpretation of kinetic estimates at homeostasis. This suggests that short-term HSC and multipotent progenitors can dynamically adjust to sustain themselves temporarily in the absence of long-term HSCs, even if they differentiate more often than they self-renew in undisturbed homeostasis. Additionally, the presence of feedback control in the model renders the system resilient against mutant invasion. Invasion barriers, however, can be overcome by a combination of age-related changes in stem cell differentiation and evolutionary niche construction dynamics based on a mutant-associated inflammatory environment. This helps us understand the evolution of e.g., TET2 or DNMT3A mutants, and how to potentially reduce mutant burden.

The bacterial flagellum as an object for optical trapping.

This letter considers the possibility of using the optical trap to study the structure and function of the microbial flagellum. The structure of the flagellum of a typical gram-negative bacterium is described in brief. A standard mathematical model based on the principle of superposition is used to describe the movement of an ellipsoidal microbial cell in a liquid medium. The basic principles of optical trapping based on the combined action of the light pressure and the gradient force are briefly clarified. Several problems related to thermal damage of living microscopic objects when the latter gets to the focus of a laser beam are shortly discussed. It is shown that the probability of cell damage depends nonlinearly on the wavelength of laser radiation. Finally, the model systems that would make it possible to study flagella of the free bacteria and the ones anchored or tethered on the surface of a solid material are discussed in detail.

Manufacture, characterization, and elucidation of drug release mechanisms of etonogestrel implants based on ethylene vinyl acetate.

In this work, etonogestrel implants were manufactured using coextrusion. The purpose of the study was to correlate changes in microstructure and transport properties that occurred in etonogestrel implants to drug release mechanisms. The implants consisted of an EVA 28 (28 % vinyl acetate) core containing dispersed and dissolved etonogestrel, and an EVA 15 (15 % vinyl acetate) skin. The drug release was determined to be via diffusion at a controlled rate and governed by implant dimensions. In-vitro release revealed evidence of supersaturation in the implant core and skin, likely from the intense mechanical energy input during the twin-screw manufacturing process. Subsequently during storage under ambient conditions, supersaturation resulted in recrystallization of drug crystals, preferentially in the implant core. Etonogestrel solubility and diffusivity in EVA were determined by permeation experiments and used for release modeling. Drug release from the EVA skin layer deviated from the predicted values due to 1) formation of a drug depletion zone in the core and 2) presence of a stagnant media layer adjacent to the skin. Drug release from implant ends was significantly faster than predicted. Air-filled pores were observed in the implant core using microCT which likely contributed to the faster release from implant ends.

Predictive value of mono-exponential and multiple mathematical models in locally advanced rectal cancer response to neoadjuvant chemoradiotherapy.

PURPOSE: This prospective study aimed to assess the predictive value of mono-exponential and multiple mathematical diffusion-weighted imaging (DWI) models in determining the response to neoadjuvant chemoradiotherapy (nCRT) in patients with locally advanced rectal cancer (LARC). METHODS: The study included 103 LARC patients scheduled for preoperative chemoradiotherapy between December 2021 and June 2023 Magnetic resonance imaging (MRI) scans were performed using a 3.0-T MR scanner, encompassing sagittal, axial, and oblique coronal T2-weighted images without fat saturation, along with DWI perpendicular to the rectum's long axis. Various DWI parameters, including apparent diffusion coefficient (ADC), stretched exponential model (SEM), continuous-time random-walk model (CTRW), and fractional-order calculus model (FROC), were measured. The pathologic complete response (pCR) rate and tumor downstaging (T-downstage) rate were determined. RESULTS: After nCRT, SEM-α, SEM-DDC, CTRW-α, CTRW-ß, CTRW-D, FROC-ß, and ADC values were significantly higher in the pCR group compared to the non-pCR group (all P < 0.05). SEM-DDC, CTRW-α, CTRW-D, FROC-ß, FROC-µ, and ADC values were significantly higher in the T-downstage group (ypT0-1) than in the non-T-downstage group (ypT2-4) (P < 0.05). The combination of CTRW (α + ß + D) exhibited the best diagnostic performance for assessing pCR after nCRT (AUC = 0.840, P < 0.001). Pre-nCRT CTRW (α + ß) demonstrated a predictive AUC of 0.652 (95%CI: 0.552-0.743), 90.3% sensitivity, and 43.1% specificity for pCR. Regarding T-downstage assessment after nCRT, the combination of CTRW (α + D) yielded the best diagnostic performance (AUC = 0.877, P = 0.048). CONCLUSION: In LARC patients, imaging markers derived from CTRW show promise in predicting tumor response before nCRT and assessing pCR after nCRT.

A Mathematical Model of Diel Activity and Long Time Survival in Phototrophic Mixed-Species Subaerial Biofilms.

Subaerial biofilms (SAB) are intricate microbial communities living on terrestrial surfaces, of interest in a variety of contexts including cultural heritage preservation, microbial ecology, biogeochemical cycling, and biotechnology. Here we propose a mathematical model aimed at better understanding the interplay between cyanobacteria and heterotrophic bacteria, common microbial SAB constituents, and their mutual dependence on local environmental conditions. SABs are modeled as thin mixed biofilm-liquid water layers sitting on stone. A system of ordinary differential equations regulates the dynamics of key SAB components: cyanobacteria, heterotrophs, polysaccharides and decayed biomass, as well as cellular levels of organic carbon, nitrogen and energy. These components are interconnected through a network of energetically dominant metabolic pathways, modeled with limitation terms reflecting the impact of biotic and abiotic factors. Daily cylces of temperature, humidity, and light intensity are considered as input model variables that regulate microbial activity by influencing water availability and metabolic kinetics. Relevant physico-chemical processes, including pH regulation, further contribute to a description of the SAB ecology. Numerical simulations explore the dynamics of SABs in a real-world context, revealing distinct daily activity periods shaped by water activity and light availability, as well as longer time scale survivability conditions. Results also suggest that heterotrophs could play a substantial role in decomposing non-volatile carbon compounds and regulating pH, thus influencing the overall composition and stability of the biofilm.

Advances in Modeling Approaches for Oral Drug Delivery: Artificial Intelligence, Physiologically-Based Pharmacokinetics, and First-Principles Models.

Oral drug absorption is the primary route for drug administration. However, this process hinges on multiple factors, including the drug's physicochemical properties, formulation characteristics, and gastrointestinal physiology. Given its intricacy and the exorbitant costs associated with experimentation, the trial-and-error method proves prohibitively expensive. Theoretical models have emerged as a cost-effective alternative by assimilating data from diverse experiments and theoretical considerations. These models fall into three categories: (i) data-driven models, encompassing classical pharmacokinetics, quantitative-structure models (QSAR), and machine/deep learning; (ii) mechanism-based models, which include quasi-equilibrium, steady-state, and physiologically-based pharmacokinetics models; and (iii) first principles models, including molecular dynamics and continuum models. This review provides an overview of recent modeling endeavors across these categories while evaluating their respective advantages and limitations. Additionally, a primer on partial differential equations and their numerical solutions is included in the appendix, recognizing their utility in modeling physiological systems despite their mathematical complexity limiting widespread application in this field.

Synthetic microbial communities: A gateway to understanding resistance, resilience, and functionality in spontaneously fermented food microbiomes.

This review delves into the intricate traits of microbial communities encountered in spontaneously fermented foods (SFF), contributing to resistance, resilience, and functionality drivers. Traits of SFF microbiomes comprise of fluctuations in community composition, genetic stability, and condition-specific phenotypes. Synthetic microbial communities (SMCs) serve as a portal for mechanistic insights and strategic re-programming of microbial communities. Current literature underscores the pivotal role of microbiomes in SFF in shaping quality attributes and preserving the cultural heritage of their origin. In contrast to starter driven fermentations that tend to be more controlled but lacking the capacity to maintain or reproduce the complex flavors and intricacies found in SFF. SMCs, therefore, become indispensable tools, providing a nuanced understanding and control over fermented food microbiomes. They empower the prediction and engineering of microbial interactions and metabolic pathways with the aim of optimizing outcomes in food processing. Summarizing the current application of SMCs in fermented foods, there is still space for improvement. Challenges in achieving stability and reproducibility in SMCs are identified, stemming from non-standardized approaches. The future direction should involve embracing standardized protocols, advanced monitoring tools, and synthetic biology applications. A holistic, multi-disciplinary approach is paramount to unleashing the full potential of SMCs and fostering sustainable and innovative applications in fermented food systems.

A Model of Linear Response with Progressive Decay Equally Suited for RiboGreen® Quantitation of RNA and Dissolution of Solid Oral Dosage forms.

A new regression model is presented which offers flexibility, freedom from subjective determinations of linear range, and very wide applicability to measurement systems of industrial importance. This "progressive decay" model starts as a deceptively simple ordinary differential equation. We show here that its solution faithfully describes real but seemingly unconnected data from a plate-based assay for quantitation of RNA with RiboGreen® and dissolution data for a triple fixed-dose combination solid oral dosage form.

Correlation of rheology and oral tribology with sensory perception of commercial hazelnut and cocoa-based spreads.

This study examined the effects of spread formulation and the structural/lubricant properties of six different commercial hazelnut and cocoa spreads on sensory perception. Rheology, tribology, and quantitative descriptive analysis (QDA) was assessed by also evaluating the correlation coefficients between the quality descriptor and the rheological and textural parameters. The viscosity was evaluated at different temperatures to better simulate conditions before and after ingestion. Tribological analysis was executed at 37°C to mimic the human oral cavity. The effect of saliva presence and the number of runs on tribological behaviors was investigated. Moreover, textural, calorimetric, and particle size distribution measurements were performed to reinforce the correlation between structural/thermal parameters (e.g., firmness, stickiness, sugar melting point) and sensory aspects. "Visual viscosity," defined as a sensory attribute evaluated prior to consumption, negatively correlated with apparent viscosity measured at 20°C and 10 s-1, whereas "body," defined during oral processing and related to creaminess, positively correlated with apparent viscosity measured at 37°C and 50 s-1. These attributes were mainly influenced by particulate microstructure and solid volume fraction within the formulation. Textural stickiness positively correlated with sensory "adhesiveness" and was related to fat composition and milk powder addition, while "sweetness" was related to sucrose content and sugar melting enthalpy. Tribological data provided meaningful information related to particle-derived attributes, as well as after-coating perception (fattiness/oiliness), thus better predicting food evolution during oral consumption.

An Introduction to Plant Cell, Tissue, and Organ Culture: Current Status and Perspectives.

Plant cell, tissue, and organ cultures (PCTOC) have been used as experimental systems in basic research, allowing gene function demonstration through gene overexpression or repression and investigating the processes involved in embryogenesis and organogenesis or those related to the potential production of secondary metabolites, among others. On the other hand, PCTOC has also been applied at the commercial level for the vegetative multiplication (micropropagation) of diverse plant species, mainly ornamentals but also horticultural crops such as potato or fruit and tree species, and to produce high-quality disease-free plants. Moreover, PCTOC protocols are important auxiliary systems in crop breeding crops to generate pure lines (homozygous) to produce hybrids for the obtention of polyploid plants with higher yields or better performance. PCTOC has been utilized to preserve and conserve the germplasm of different crops or threatened species. Plant genetic improvement through genetic engineering and genome editing has been only possible thanks to the establishment of efficient in vitro plant regeneration protocols. Different companies currently focus on commercializing plant secondary metabolites with interesting biological activities using in vitro PCTOC. The impact of omics on PCTOC is discussed.

Modeling antigen-specific T cell dynamics following Hepatitis B Vaccination indicates differences between conventional and regulatory T cell dynamics.

Our study aims to investigate the dynamics of conventional memory T cells (Tconv) and regulatory memory T cells (Treg) following activation, and to explore potential differences between these two cell types. To achieve this, we developed advanced statistical mixed models based on mathematical models of ordinary differential equations (ODE), which allowed us to transform post-vaccination immunological processes into mathematical formulas. These models were applied to in-house data from a de novo Hepatitis B vaccination trial. By accounting for inter- and intra-individual variability, our models provided good fits for both antigen-specific Tconv and Treg cells, overcoming the challenge of studying these complex processes. Our modeling approach provided a deeper understanding of the immunological processes underlying T cell development after vaccination. Specifically, our analysis revealed several important findings regarding the dynamics of Tconv and Treg cells, as well as their relationship to seropositivity for Herpes Simplex Virus Type 1 (HSV-1) and Epstein-Barr Virus (EBV), and the dynamics of antibody response to vaccination. Firstly, our modeling indicated that Tconv dynamics suggest the existence of two T cell types, in contrast to Treg dynamics where only one T cell type is predicted. Secondly, we found that individuals who converted to a positive antibody response to the vaccine earlier had lower decay rates for both Tregs and Tconv cells, which may have important implications for the development of more effective vaccination strategies. Additionally, our modeling showed that HSV-1 seropositivity negatively influenced Tconv cell expansion after the second vaccination, while EBV seropositivity was associated with higher Treg expansion rates after vaccination. Overall, this study provides a critical foundation for understanding the dynamic processes underlying T cell development after vaccination.

Analysing vaccine efficacy evaluated in phase 3 clinical trials carried out during outbreaks.

In this paper we examine several definitions of vaccine efficacy (VE) that we found in the literature, for diseases that express themselves in outbreaks, that is, when the force of infection grows in time, reaches a maximum and then vanishes. The fact that the disease occurs in outbreaks results in several problems that we analyse. We propose a mathematical model that allows the calculation of VE for several scenarios. Vaccine trials usually needs a large number of volunteers that must be enrolled. Ideally, all volunteers should be enrolled in approximately the same time, but this is generally impossible for logistic reasons and they are enrolled in a fashion that can be replaced by a continuous density function (for example, a Gaussian function). The outbreak can also be replaced by a continuous density function, and the use of these density functions simplifies the calculations. Assuming, for example Gaussian functions, one of the problems one can immediately notice is that the peak of the two curves do not occur at the same time. The model allows us to conclude: First, the calculated vaccine efficacy decreases when the force of infection increases; Second, the calculated vaccine efficacy decreases when the gap between the peak in the force of infection and the peak in the enrollment rate increases; Third, different trial protocols can be simulated with this model; different vaccine efficacy definitions can be calculated and in our simulations, all result are approximately the same. The final, and perhaps most important conclusion of our model, is that vaccine efficacy calculated during outbreaks must be carefully examined and the best way we can suggest to overcome this problem is to stratify the enrolled volunteer's in a cohort-by-cohort basis and do the survival analysis for each cohort, or apply the Cox proportional hazards model for each cohort.

Modeling Glucose, Insulin, C-Peptide, and Lactate Interplay in Adolescents During an Oral Glucose Tolerance Test.

BACKGROUND: Lactate is not considered just a "waste product" of anaerobic glycolysis anymore. It has been proved to play a key role in several metabolic diseases, such as in the metabolic dysfunction-associated steatotic liver disease, obesity, and diabetes. The capability of simulating glucose-insulin-lactate interaction would be useful to design and test drugs targeting lactate metabolism in such pathological conditions. Minimal models are available, which describe and quantify glucose-lactate interaction but models to simulate postprandial glucose-insulin-C-peptide-lactate time courses are missing. The aim of this study is to fill this gap. METHODS: Starting from the Padova Type 2 Diabetes Simulator (T2DS), we first added a description of glucose-lactate kinetics and then created a population of 100 in silico subjects to match glucose-insulin-C-peptide-lactate data of 44 adolescents with/without obesity who underwent a standard oral glucose tolerance test (OGTT) of 75 g. RESULTS: The developed model accurately predicts all molecules time courses, guaranteeing precise model parameter estimates (percent coefficient of variation [CV%] median [25th-75th percentile] = 19 [9-29]%). The generated in silico population shows good agreement with the clinical data in terms of area under the curve (AUC) (P = .6, .6, .9, .6 for glucose, insulin, C-peptide, and lactate, respectively) and parameter distributions (P > .1). CONCLUSIONS: We have developed a simulator to describe glucose, insulin, C-peptide, and lactate kinetics during an OGTT, which captures the behavior of a real population of adolescents with/without obesity both in terms of average and intersubject variability. Such simulator can be used to investigate the pharmacodynamics of drugs targeting lactate metabolic pathway in various pathological conditions.

Modeling the transmission of antibiotic-resistant Enterobacterales in the community: A systematic review.

BACKGROUND: Antibiotic-resistant Enterobacterales (ARE) are a public health threat worldwide. Dissemination of these opportunistic pathogens has been largely studied in hospitals. Despite high prevalence of asymptomatic colonization in the community in some regions of the world, less is known about ARE acquisition and spread in this setting. As explaining the community ARE dynamics has not been straightforward, mathematical models can be key to explore underlying phenomena and further evaluate the impact of interventions to curb ARE circulation outside of hospitals. METHODS: We conducted a systematic review of mathematical modeling studies focusing on the transmission of AR-E in the community, excluding models only specific to hospitals. We extracted model features (population, setting), formalism (compartmental, individual-based), biological hypotheses (transmission, infection, antibiotic impact, resistant strain specificities) and main findings. We discussed additional mechanisms to be considered, open scientific questions, and most pressing data needs. RESULTS: We identified 18 modeling studies focusing on the human transmission of ARE in the community (n=11) or in both community and hospital (n=7). Models aimed at (i) understanding mechanisms driving resistance dynamics; (ii) identifying and quantifying transmission routes; or (iii) evaluating public health interventions to reduce resistance. To overcome the difficulty of reproducing observed ARE dynamics in the community using the classical two-strains competition model, studies proposed to include mechanisms such as within-host strain competition or a strong host population structure. Studies inferring model parameters from longitudinal carriage data were mostly based on models considering the ARE strain only. They showed differences in ARE carriage duration depending on the acquisition mode: returning travelers have a significantly shorter carriage duration than discharged hospitalized patient or healthy individuals. Interestingly, predictions across models regarding the success of public health interventions to reduce ARE rates depended on pathogens, settings, and antibiotic resistance mechanisms. For E. coli, reducing person-to-person transmission in the community had a stronger effect than reducing antibiotic use in the community. For Klebsiella pneumoniae, reducing antibiotic use in hospitals was more efficient than reducing community use. CONCLUSIONS: This study raises the limited number of modeling studies specifically addressing the transmission of ARE in the community. It highlights the need for model development and community-based data collection especially in low- and middle-income countries to better understand acquisition routes and their relative contribution to observed ARE levels. Such modeling will be critical to correctly design and evaluate public health interventions to control ARE transmission in the community and further reduce the associated infection burden.

Deep brain stimulation pulse sequences to optimally modulate frequency-specific neural activity.

Objective. Precise neuromodulation systems are needed to identify the role of neural oscillatory dynamics in brain function and to advance the development of brain stimulation therapies tailored to each patient's signature of brain dysfunction. Low-frequency, local field potentials (LFPs) are of increasing interest for the development of these systems because they can reflect the synaptic inputs to a recorded neuronal population and can be chronically recorded in humans. In this computational study, we aim to identify stimulation pulse patterns needed to optimally maximize the suppression or amplification of frequency-specific neural activity.Approach. We derived DBS pulse patterns to minimize or maximize the 2-norm of frequency-specific neural oscillations using a generalized mathematical model of spontaneous and stimulation-evoked LFP activity, and a subject-specific model of neural dynamics in the pallidum of a Parkinson's disease patient. We leveraged convex and mixed-integer optimization tools to identify these pulse patterns, and employed constraints on the pulse frequency and amplitude that are required to keep electrical stimulation within its safety envelope.Main results. Our analysis revealed that a combination of phase, amplitude, and frequency pulse modulation is needed to attain optimal suppression or amplification of the targeted oscillations. Phase modulation is sufficient to modulate oscillations with a constant amplitude envelope. To attain optimal modulation for oscillations with a time-varying envelope, a trade-off between frequency and amplitude pulse modulation is needed. The optimized pulse sequences were invariant to changes in the dynamics of stimulation-evoked neural activity, including changes in damping and natural frequency or complexity (i.e. generalized vs. patient-specific model).Significance. Our results provide insight into the structure of pulse patterns for future closed-loop brain stimulation strategies aimed at controlling neural activity precisely and in real-time.

Experimentally validated modeling of dynamic drug-hERG channel interactions reproducing the binding mechanisms and its importance in action potential duration.

BACKGROUND AND OBJECTIVE: Assessment of drug cardiotoxicity is critical in the development of new compounds and modeling of drug-binding dynamics to hERG can improve early cardiotoxicity assessment. We previously developed a methodology to generate Markovian models reproducing preferential state-dependent binding properties, trapping dynamics and the onset of IKr block using simple voltage clamp protocols. Here, we test this methodology with real IKr blockers and investigate the impact of drug dynamics on action potential prolongation. METHODS: Experiments were performed on HEK cells stably transfected with hERG and using the Nanion SyncroPatch 384i. Three protocols, P-80, P0 and P 40, were applied to obtain the experimental data from the drugs and the Markovian models were generated using our pipeline. The corresponding static models were also generated and a modified version of the O´Hara-Rudy action potential model was used to simulate the action potential duration. RESULTS: The experimental Hill plots and the onset of IKr block of ten compounds were obtained using our voltage clamp protocols and the models generated successfully mimicked these experimental data, unlike the CiPA dynamic models. Marked differences in APD prolongation were observed when drug effects were simulated using the dynamic models and the static models. CONCLUSIONS: These new dynamic models of ten well-known IKr blockers constitute a validation of our methodology to model dynamic drug-hERG channel interactions and highlight the importance of state-dependent binding, trapping dynamics and the time-course of IKr block to assess drug effects even at the steady-state.

Mosquito species identity matters: unraveling the complex interplay in vector-borne diseases.

BACKGROUND: Research on vector-borne diseases has traditionally centred on a limited number of vertebrate hosts and their associated pathogens, often neglecting the broader array of vectors within communities. Mosquitoes, with their vast species diversity, hold a central role in disease transmission, yet their capacity to transmit specific pathogens varies considerably among species. Quantitative modelling of mosquito-borne diseases is essential for understanding transmission dynamics and requires the necessity of incorporating the identity of vector species into these models. Consequently, understanding the role of different species of mosquitoes in modelling vector-borne diseases is crucial for comprehending pathogen amplification and spill-over into humans. This comprehensive overview highlights the importance of considering mosquito identity and emphasises the essential need for targeted research efforts to gain a complete understanding of vector-pathogen specificity. METHODS: Leveraging the recently published book, 'Mosquitoes of the World', I identified 19 target mosquito species in Europe, highlighting the diverse transmission patterns exhibited by different vector species and the presence of 135 medically important pathogens. RESULTS: The review delves into the complexities of vector-pathogen interactions, with a focus on specialist and generalist strategies. Furthermore, I discuss the importance of using appropriate diversity indices and the challenges associated with the identification of correct indices. CONCLUSIONS: Given that the diversity and relative abundance of key species within a community significantly impact disease risk, comprehending the implications of mosquito diversity in pathogen transmission at a fine scale is crucial for advancing the management and surveillance of mosquito-borne diseases.

Utilization of diffusion-weighted derived mathematical models to predict prognostic factors of resectable rectal cancer.

PURPOSE: This study explored models of monoexponential diffusion-weighted imaging (DWI), diffusion kurtosis imaging (DKI), stretched exponential (SEM), fractional-order calculus (FROC), and continuous-time random-walk (CTRW) as diagnostic tools for assessing pathological prognostic factors in patients with resectable rectal cancer (RRC). METHODS: RRC patients who underwent radical surgery were included. The apparent diffusion coefficient (ADC), the mean kurtosis (MK) and mean diffusion (MD) from the DKI model, the distributed diffusion coefficient (DDC) and α from the SEM model, D, ß and u from the FROC model, and D, α and ß from the CTRW model were assessed. RESULTS: There were a total of 181 patients. The area under the receiver operating characteristic (ROC) curve (AUC) of CTRW-α for predicting histology type was significantly higher than that of FROC-u (0.780 vs. 0.671, p = 0.043). The AUC of CTRW-α for predicting pT stage was significantly higher than that of FROC-u and ADC (0.786 vs.0.683, p = 0.043; 0.786 vs. 0.682, p = 0.030), the difference in predictive efficacy of FROC-u between ADC and MK was not statistically significant [0.683 vs. 0.682, p = 0.981; 0.683 vs. 0.703, p = 0.720]; the difference between the predictive efficacy of MK and ADC was not statistically significant (p = 0.696). The AUC of CTRW (α + ß) (0.781) was significantly higher than that of FROC-u (0.781 vs. 0.625, p = 0.003) in predicting pN stage but not significantly different from that of MK (p = 0.108). CONCLUSION: The CTRW and DKI models may serve as imaging biomarkers to predict pathological prognostic factors in RRC patients before surgery.

Prediction and control of cholera outbreak: Study case of Cameroon.

This paper deals with the problem of the prediction and control of cholera outbreak using real data of Cameroon. We first develop and analyze a deterministic model with seasonality for the cholera, the novelty of which lies in the incorporation of undetected cases. We present the basic properties of the model and compute two explicit threshold parameters R¯0 and R_0 that bound the effective reproduction number R0, from below and above, that is R_0≤R0≤R¯0. We prove that cholera tends to disappear when R¯0≤1, while when R_0>1, cholera persists uniformly within the population. After, assuming that the cholera transmission rates and the proportions of newly symptomatic are unknown, we develop the EnKf approach to estimate unmeasurable state variables and these unknown parameters using real data of cholera from 2014 to 2022 in Cameroon. We use this result to estimate the upper and lower bound of the effective reproduction number and reconstructed active asymptomatic and symptomatic cholera cases in Cameroon, and give a short-term forecasts of cholera in Cameroon until 2024. Numerical simulations show that (i) the transmission rate from free Vibrio cholerae in the environment is more important than the human transmission and begin to be high few week after May and in October, (ii) 90% of newly cholera infected cases that present the symptoms of cholera are not diagnosed and (iii) 60.36% of asymptomatic are detected at 14% and 86% of them recover naturally. The future trends reveals that an outbreak appeared from July to November 2023 with the number of cases reported monthly peaked in October 2023. An impulsive control strategy is incorporated in the model with the aim to avoid or prevent the cholera outbreak. In the first year of monitoring, we observed a reduction of more than 75% of incidences and the disappearance of the peaks when no control are available in Cameroon. A second monitoring of control led to a further reduction of around 60% of incidences the following year, showing how impulse control could be an effective means of eradicating cholera.