On the date of the epidemic peak.

Epidemiologists have used the timing of the peak of an epidemic to guide public health interventions. By determining the expected peak time, they can allocate resources effectively and implement measures such as quarantine, vaccination, and treatment at the right time to mitigate the spread of the disease. The peak time also provides valuable information for those modeling the spread of the epidemic and making predictions about its future trajectory. In this study, we analyze the time needed for an epidemic to reach its peak by presenting a straightforward analytical expression. Utilizing two epidemiological models, the first is a generalized $ SEIR $ model with two classes of latent individuals, while the second incorporates a continuous age structure for latent infections. We confirm the conjecture that the peak occurs at approximately $ T\sim(\ln N)/\lambda $, where $ N $ is the population size and $ \lambda $ is the largest eigenvalue of the linearized system in the first model or the unique positive root of the characteristic equation in the second model. Our analytical results are compared to numerical solutions and shown to be in good agreement.

On a two-strain epidemic model involving delay equations.

We propose an epidemiological model for the interaction of either two viruses or viral strains with cross-immunity, where the individuals infected by the first virus cannot be infected by the second one, and without cross-immunity, where a secondary infection can occur. The model incorporates distributed recovery and death rates and consists of integro-differential equations governing the dynamics of susceptible, infectious, recovered, and dead compartments. Assuming that the recovery and death rates are uniformly distributed in time throughout the duration of the diseases, we can simplify the model to a conventional ordinary differential equation (ODE) model. Another limiting case arises if the recovery and death rates are approximated by the delta-function, thereby resulting in a new point-wise delay model that incorporates two time delays corresponding to the durations of the diseases. We establish the positiveness of solutions for the distributed delay models and determine the basic reproduction number and an estimate for the final size of the epidemic for the delay model. According to the results of the numerical simulations, both strains can coexist in the population if the disease transmission rates for them are close to each other. If the difference between them is sufficiently large, then one of the strains dominates and eliminates the other one.

The influence of immune cells on the existence of virus quasi-species.

This article investigate a nonlocal reaction-diffusion system of equations modeling virus distribution with respect to their genotypes in the interaction with the immune response. This study demonstrates the existence of pulse solutions corresponding to virus quasi-species. The proof is based on the Leray-Schauder method, which relies on the topological degree for elliptic operators in unbounded domains and a priori estimates of solutions. Furthermore, linear stability analysis of a spatially homogeneous stationary solution identifies the critical conditions for the emergence of spatial and spatiotemporal structures. Finally, numerical simulations are used to illustrate nonlinear dynamics and pattern formation in the nonlocal model.

Nonlinear diffusion in multi-patch logistic model.

We examine a multi-patch model of a population connected by nonlinear asymmetrical migration, where the population grows logistically on each patch. Utilizing the theory of cooperative differential systems, we prove the global stability of the model. In cases of perfect mixing, where migration rates approach infinity, the total population follows a logistic law with a carrying capacity that is distinct from the sum of carrying capacities and is influenced by migration terms. Furthermore, we establish conditions under which fragmentation and nonlinear asymmetrical migration can lead to a total equilibrium population that is either greater or smaller than the sum of carrying capacities. Finally, for the two-patch model, we classify the model parameter space to determine if nonlinear dispersal is beneficial or detrimental to the sum of two carrying capacities.

A model of a fishery with fish storage and variable price involving delay equations.

We propose a bio-economic model of a fishery describing the variations of the fish stock, the fishing effort and the price of the resource on the market supposed to depend on supply and demand. The originality of this model comes from taking into account the storage of part of the resource for a certain time before being put up for sale on the market. Taking into account the supposedly fast price dynamics compared to the other mechanisms involved and after integration of the stock equation, the system is reduced to a system of two delayed differential equations. The qualitative analysis of the model is carried out with the search for equilibrium points and the study of their stability. The study shows the existence of a catastrophic equilibrium corresponding to the extinction of the resource and one or two sustainable fishery equilibrium points that can coexist under certain conditions. The model shows that storing part of the resource makes it possible to avoid a catastrophic situation with the extinction of the fish stock and to stabilize the fishery in the long term. The study also shows that the price variation of the resource has a stabilizing effect by avoiding the appearance of periodic solutions associated with a stable limit cycle surrounding a sustainable fishery equilibrium point resulting from a Hopf bifurcation, which is contrary to the case without price variation where this is possible.

On the Threshold of Release of Confinement in an Epidemic SEIR Model Taking into Account the Protective Effect of Mask.

We present a classic SEIR model taking into account the daily movements of individuals in different places. The model also takes into account partial confinement of individuals. This model is coupled with a model of protection against the epidemic by the use of masks. We are studying the effects of combined confinement and protection measures on the dynamics of the epidemic. We consider a constant proportion of asymptomatic people. We assume that symptomatic infected people may change their urban travel behavior due to the disease which causes them to travel less to places where they used to move and to stay at home more often. We present a sensitivity study with respect to the parameters. We show that the combination of the use of masks with almost complete release of confinement makes it possible to avoid the occurrence of a secondary peak of the epidemic. The model predicts that a total release of confinement can be successful for an epidemic of [Formula: see text] if on average a proportion of [Formula: see text] of the population wears masks of [Formula: see text] efficacy. However, if [Formula: see text] of the population remains confined, the same goal can be achieved with a proportion of [Formula: see text] of the population wearing masks with efficacy of the order of [Formula: see text].

Transmission dynamics of COVID-19 in Algeria: The impact of physical distancing and face masks.

We propose an SIR epidemic model taking into account prevention measures against coronavirus disease 2019 (COVID-19) such as wearing masks and respecting safety distances. We look for the conditions to avoid a second epidemic peak in the phase of release from confinement. We derive equations for the critical levels of mask efficiency, mask adoption (fraction of population wearing masks) and fraction of population engaging in physical distancing that lower the basic reproduction number ℜ 0 to unity. Conclusions: For ℜ 0 = 2.5, if at least 40% of people wear masks with efficiency 50%, and at least 20% of the population without masks (or anti-maskers) respect physical distancing measures, the effective reproduction number can be reduced to less than 1 and COVID-19 infections would plummet. The model predicts also that if at least half of the people respecting physical distancing, COVID-19 outbreaks with ℜ 0 of about 3, would be theoretically extinguished without wearing masks. The results of this study provide an alternative explanation for the spread of the disease, and suggest some valuable policy recommendations about the control strategies applied to mitigate disease transmission.

HER-2 status of circulating tumor cells in a metastatic breast cancer cohort: A comparative study on characterization techniques.

BACKGROUND: Personalized targeted treatment in metastatic breast cancer relies on accurate assessment of molecular aberrations, e.g. overexpression of Human Epidermal growth factor Receptor 2 (HER-2). Molecular interrogation of circulating tumor cells (CTCs) can provide an attractive alternative for real-time biomarker assessment. However, implementation of CellSearch-based HER-2 analysis has been limited. Immunofluorescent (IF) image interpretation is crucial, as different HER-2 categories have been described. Major questions in CTC research are how these IF categories reflect gene expression and amplification, and if we should consider 'medium' HER-2 expressing CTCs for patient selection. METHODS: Tumor cells from spiked cell lines (n = 8) and CTCs (n = 116 samples) of 85 metastatic breast cancer patients were enriched using CellSearch. Comparative analysis of HER-2 expression by IF imaging (ACCEPT, DEPArray, and visual scoring) with qRT-PCR and HER-2/neu FISH was performed. RESULTS: Automated IF HER-2-profiling by DEPArray and ACCEPT delivered comparable results. There was a 98% agreement between 17 trained observers (visual scoring) and ACCEPT considering HER-2neg and HER-2high expressing CTCs. However, 89% of HER-2med expressing CTCs by ACCEPT were scored negative by observers. HER-2high expressing tumor cells demonstrated HER-2/neu gene amplification, whereas HER-2neg and HER-2med expressing tumor cells and CTCs by ACCEPT were copy-number neutral. All patients with HER-2-positive archival tumors had ≥1 HER-2high expressing CTCs, while 80% of HER-2-negative patients did not. High relative gene expression of HER-2 measured on enriched CTC lysates correlated with having ≥1 HER-2high expressing CTCs. CONCLUSION: Automated images analysis has enormous potential for clinical implementation. HER-2 characterization and clinical trial design should be focused on HER-2high expressing CTCs.

Modeling the imported malaria to north Africa and the absorption effect of the immigrants.

As Malaria represents one of the major health burdens in Africa, there is a risk of reappearance of this vector-borne disease in malaria-free or low risk countries such as those in North Africa. One of the factors that can lead to this situation is the flow of sub-Saharan immigrants trying to reach Europe through North Africa. In this work, we investigate such a possibility via a mathematical model. We assume that the immigrant (non-locals) population has a carrying capacity that limits their numbers in the host country, and we study how they might contribute to the disease spread. Our analysis gave conditions of the persistence of the disease and showed that the non-local population could have a positive effect by reducing the spread of Malaria.

Effect of hawk-dove game on the dynamics of two competing species.

Outcomes of interspecific competition, and especially the possibility of coexistence, have been extensively studied in theoretical ecology because of their implications in community assemblages. During the last decades, the influence of different time scales through the local/regional dynamics of animal communities has received an increasing attention. Nevertheless, different time scales involved in interspecific competition can result form other processes than spatial dynamics. Here, we envision and analyze a new theoretical framework that couples a game theory approach for competition with a demographic model. We take advantage of these two time scales to derive a reduced model governing the total densities of the two populations and we study how these two time scales interfere and influence outcomes of species competition. We find that a competition process occurring on a faster time scale than demography yields a "priority effect" where the first species introduced outcompetes the other one. We then confirm previous findings stipulating that species coexistence is favored by large difference in time scales because the extinction/recolonization process. Our results then highlight that an integration of demographic and competition time scales at both local and regional levels is mandatory to explain communities assemblages and should become a research priority.

Basic reproduction ratio for a fishery model in a patchy environment.

We present a dynamical model of a multi-site fishery. The fish stock is located on a discrete set of fish habitats where it is catched by the fishing fleet. We assume that fishes remain on fishing habitats while the fishing vessels can move at a fast time scale to visit the different fishing sites. We use the existence of two time scales to reduce the dimension of the model : we build an aggregated model considering the habitat fish densities and the total fishing effort. We explore a regulation procedure, which imposes an average residence time in patches. Several equilibria exist, a Fishery Free Equilibria (FFEs) as well as a Sustainable Fishery Equilibria (SFEs). We show that the dynamics depends on a threshold which is similar to a basic reproduction ratio for the fishery. When the basic reproduction ratio is less or equal to 1, one of the FFEs is globally asymptotically stable (GAS), otherwise one of the SFEs is GAS.

Optimal number of sites in multi-site fisheries with fish stock dependent migrations.

We present a stock-effort dynamical model of a fishery subdivided into fishing zones. The stock corresponds to a fish population moving between these zones, on which they are harvested by fishing fleets. We consider a linear chain of identical fishing zones. Fish movements between the zones, as well as vessels displacements, are assumed to take place at a faster time scale than the variation of the stock and the change of the fleet size. The vessels movements between the fishing areas are assumed to be stock dependent, i.e. the larger the stock density is in a zone the more vessels tends to remain in it. We take advantage of these two time scales to derive a reduced model governing the dynamics of the total harvested stock and the total fishing effort. Under some assumption, we obtain either a stable equilibrium or a stable limit cycle which involves large cyclic variations of the total fish stock and fishing effort. We show that there exists an optimal number of fishing zones that maximizes the total catch at equilibrium. We discuss the results in relation to fish aggregating devices (FADs) fisheries.

[Retroperitoneal laparoscopic treatment of parapelvic renal cysts: report of 5 cases]. / Traitement laparoscopique par voie rétropéritonéale des kystes para-pyéliques symptomatiques (a propos de 5 cas).

OBJECTIVES: Renal cysts of the sinuses or parapelvic cysts constitute a rare form of renal cyst, usually associated with low back pain. Symptomatic forms may be treated by percutaneous aspiration, but the treatment of these cysts has changed considerably over recent years due to the proximity of the renal hilum. Percutaneous treatment is now contraindicated due to its high complication rate, and open surgery is an invasive technique. Laparoscopy appears to be the most appropriate and most effective solution. PATIENTS AND METHODS: The authors report five cases of parapelvic renal cysts all presenting with renal colic and diagnosed by ultrasound, and confirmed by CT in three cases. Treatment consisted of retroperitoneal laparoscopy using four trocars allowing cyst resection with no intraoperative complications or conversion. RESULTS: The mean operating time was 55 minutes (range: 40 to 70 minutes). The postoperative course was uneventful and all patients were discharged on postoperative D1 or D2. No recurrence was observed after a mean follow-up of 6 months (range: 3 to 15 months). CONCLUSION: Retroperitoneal laparoscopic treatment of parapelvic renal cysts is an effective approach, with a low morbidity and less postoperative pain, a short convalescence period and good cosmetic results.

[Congenital male urethral diverticulum]. / Diverticule congénital de l'uréthre chez l'adulte.

The male urethral diverticulum is a rare affection. The authors report one case of congenital urethral diverticulum. The diagnosis was approved by clinical examination and urethrocystography. Treatment was based by resection of the diverticulum and urethrography. On the basis of this case, the authors discuss the incidence, diagnosis and therapeutic aspects of this disease.

[Inflammatory myofibroblastic tumours of the bladder]. / Les tumeurs myofibroblastiques inflammatoires de la vessie.

The inflammatory myofibroblastic tumour of the bladder is a rare benign affection that interests mainly young adults. Its etiopathogeny remains unknown, but its tumoral origin was evocated recently by Griffin (1999), incriminating a chromosomic abnormality involving the ALK gene. We will discuss the etiopathogenic, anatopathological and therapeutical aspects of this lesion for which the diagnosis is histological and the treatment remains conservative with a good prognosis.