Melanoma is considered one of the most aggressive types of cancer due to its high propensy for metastasis, which significantly reduces survival chances when detected late. Moreover, melanoma exhibits strong immunogenic characteristics, complicating its treatment, increasing the need to develop more effective techniques of therapy. In the field of oncology, mathematical modeling enables the analysis and distinction of the various mechanisms involved in tumor progression. This allows the analysis of numer-ous scenarios, which would be impractical experimentally. The main objective of this study is to develop a mathematical model that describes melanoma dynamics in the presence of Tumor-Associated Macrophages (TAM) and Chimeric Antigen Receptor (CAR) T-cell immunotherapy. The goal is to assess why this therapy often falls short in erradicating solid tumors like melanoma and to understand the role of TAM in this failure. This research encompasses stability analysis of the equilibrium points of the model, sensitivity analysis of its parameters, and the examination of numerical solutions. Our results showed that immunosuppression caused by TAM has a negative impact on the effectiveness of the dose and varying the cytotoxicity of CART-cells together with dose. Adjusting CAR T-cell cytotoxicity and treatment dosage may enhance tumor control, with the initial tumor burden playing a crucial role in treatment effectiveness.

This study investigates numerically the interaction between a Gaussian pulse and variable topography using the linear Euler equations. The impact of topography variation on the amplitude and behavior of the wave pulse is examined through numerical simulations and statistical analysis. On one hand, we show that for slowly varying topographies, the incoming pulse almost retains its shape, and little energy is transferred to the small reflected waves. On the other hand, we demonstrate that for rapidly varyingtopographies, the shape of the pulse is destroyed, which is different from previous studies.

In this work, we provide some sufficient conditions to study the global asymptotic stability of the endemic equilibrium for certain models in mathematical epidemiology with nonlinear incidence and removal functions. We also present numerical examples in order to illustrate our results.

This paper proposes an integrated control model that enables the pesticide use according to the prey density and the insertion of the natural enemy, the predators, by fuzzy linear programming. The fall armyworm Spodoptera frugiperda (Lepidoptera: Noctuidae) is one of the main resistant pests of corn, which can cause damage to the productivity up to 34%. The control is strictly chemical.

Segmentation is one of the inferential applications for detecting patterns indigital images, which has been widely used in the health area. Thresholding, a type of segmentation, consists of separating the gray groups of an image, through one or more thresholds applied to the histogram. Thus, we used the gray tone with the lowest Fuzzy Divergence found to apply the enhancement method, through membership values. This paper presents a method to assist physicians in interpreting lung radiography images, especially in the pandemic caused by COVID-19, when enhancing lung images. In addition, we consulted with a group of medical experts who saw an improvement in image quality, providing the perception of detail in the enhanced image compared to the original image.

In this work, inspired by Ramanujan’s fifth order Mock Theta function f1(q), we define acollection of functions and look at them as generating functions for partitions of some integer n containing at least m parts equal to each one of the numbers from 1 to its greatest part s, with no gaps.We set a two-line matrix representation for these partitions for any m ≥ 2 and collect the values of the sum of the entries in the second line of those matrices. These sums contain information about some parts of the partitions, which lead us to closed formulas for the number of partitions generated by our functions, and partition identities involving other simpler and well known partition functions.

During the first months of 2020 SARS-CoV-2 spread to all continents, virtually reaching all countries. In the subsequent months, new variants emerged in different regions of the world. A mathematical model based on the Covid-19 natural history encompassing the age-dependent fatality was applied to evaluate SARS-CoV-2 transmissibility and virulence. Transmissibility was assessed by calculating the basic reproduction number R0 and virulence by counting the proportion of severe Covid-19 cases and deaths. The model parameters were adjusted against the data observed in the state of São Paulo, Brazil, considering two different levels of virulence. The severe Covid-19 cases and deaths were three times higher and R0 was 25% lower when the more virulent SARS-CoV-2 variant was compared to the less virulent variant. However, under the high-virulence scenario the number of transmitting individuals is 25% lower, mainly due to the isolation of symptomatic individuals. The corollary that transmission increases in the low virulence scenario is also true. The estimated parameters, using data from São Paulo up to May 13, 2020, showed that the Covid-19 epidemic predicted with low virulence SARS-CoV-2 transmission matched the observed data just before the beginning of the relaxation, which occurred by mid-June 2020. The assessment of the interplay between transmissibility can be applied to explain in somehow the appearance of gamma and omicron variants of concern in São Paulo.

In 2019, more than 90% of the world’s population was living in places where pollutantconcentrations exceeded the air-quality guidelines. Anthropogenic activity has been the main cause of climate change in the last 20 years, especially in urban centres where industrial activities and motorized traffic mainly occur. This article presents a study of air pollutant dispersion by computational fluid dynamics modelling using OpenFOAM for urban street canyon simulations. The aim of this study was to investigate the influence of vegetation on natural ventilation, dispersion and CO2 mitigation. The behavior of pollutants was modeled by the Reynolds-averaged Navier–Stokes equations (RANS) and the k−ε fluid turbulence model. The results indicate that aerodynamic effects are more important at lower pollutant wind velocities, as they reduce turbulent dispersion and allow a higher reduction in the concentration of air pollutants. In addition, the direction of the wind, relative to the main axis of the street, had a significant impact on the results found. In general, in the presence of trees, perpendicular winds can lead to higher concentration of pollutants, while parallel winds allow improve air quality, considerably reducing those pollutant concentrations.

Aedes aegypti is the main vector of multiple diseases, such as dengue, yellow fever, Zika, and chikungunya. Diseases associated with mosquitoes have been growing in recent years, with more than one-third of the world population at risk. Control techniques have been studied to prevent the spread of the Aedes aegypti, such that new formula and how to use adulticides and larvicides, among others. This paper proposes a novel approach in the field of partial differential equations and optimization. We consider a two-dimensional diffusion-reaction model that describes the interaction between aquatic and adult female stages spreading across a domain with parameters dependent on rainfall and temperature. We also formulate a mono-objective and multiobjective optimization problem to minimize the Aedes aegypti populations and the control, considering the application of adulticides and larvicides, using actual data from the city of Lavras/Brazil. The operator splitting technique is used to solve the diffusion-reaction system, coupling finite difference and the fourth-order Runge-Kutta method and optimal solutions were searched by using the Real-Biased Genetic Algorithm and Non-dominated Sorting Genetic Algorithm -II. Numerical results show significant reduction of the Aedes aegypti population.

This work is concerned with the Cauchy problem for a Zakharov system with initial data in Sobolev spaces H^k(\R^d)×H^l(\R^d)×H^l−1(\R^d).We recall the well-posedness and ill-posedness results known to date and establish new ill-posedness results.We prove C^2 ill-posedness for some new indices (k, l) ∈ \R^2. Moreover, our results are valid in arbitrary dimension. We believe that our detailed proofs are built on a methodical approach and can be adapted to obtain similar results for other systems and equations.