In this paper, we propose a fractional order mathematical model in the sense of Caputo for the transmission dynamics of cotton disease caused by the jassid Amrasca biguttula. In this model, which takes into account disease transmission through vegetative reproduction, the cotton population is divided into susceptible (S_c), latent (L_c), and infected (I_c) individuals. The Amrasca biguttula jassid population is divided into susceptible (S_a) and infected (I_a) individuals. Through the mathematical analysis of the model, we show that the system is well posed from both the mathematical and epidemiological perspectives. After determining the basic reproduction number R_0 and the disease-free equilibrium E_s, we study the local and global stability of the equilibrium point. Sensitivity analysis is performed to identify the most influential parameter of the model, particularly for disease prevention. Finally, numerical simulations are carried out to illustrate and validate the analytical results.

This special issue presents a curated selection of original research contributions originating from the International Conference on Modelling and Differential Equations (CIMODEQS-2025), held at the Institut National Polytechnique Félix Houphouët-Boigny (INP-HB), Yamoussoukro, Ivory Coast, from April 22–24, 2025. The conference convened under the thematic focus “Modelling, Differential Equations and Impacts on Society,” fostering interdisciplinary dialogue between mathematical theory, computational applications, and societal challenges.

A family of polynomials refers to an infinite collection of polynomials with integer coefficients, typically defined in a parametric form. Constructing such a family in which all elements are irreducible is a major challenge, especially when constraints are imposed both on their coefficients and on the location of their complex roots. In this article, we present explicit families of irreducible polynomials of height equal to 1, whose Mahler measure is strictly greater than 1, and whose Graeffe-Dandelin transforms have prescribed heights. More precisely, we construct a family of irreducible polynomials that provides an affirmative answer to a question recently raised in the literature: does there exist an infinite number of irreducible polynomials P, of height equal to 1, such that \M(P) > 1, \delta(P) = 1, and the Graeffe transform \cG P also has height 1?

In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal generators subset. As an application, we study and analyze several classical problems in additive number theory on the semiring of non-negative integers by this algebraic and combinatory idea, and provide new proofs in more simple and direct way for several classical results in number theory. Some further questions are also presented and discussed.

This study presents an innovation in the use of a native Ecuadorian nanoporous material known as allophane for the reprocessing of greenhouse plastics to obtain a functional polymer that allows for reuse, improving its mechanical properties and/or increasing its lifespan. By achieving this objective, three problems are simultaneously addressed: 1) the need to recycle used plastics in a prominent Ecuadorian flower company committed to environmental preservation, 2) the scientific viability work carried out by the Central University of Ecuador, and 3) the industrial application of recycled plastics and pellet production. Blown film extrusion was used to prepare low-density polyethylene sheets with different amounts of Ecuadorian allophane microparticles (30±5 micrometers) (0.1%, 0.3%, and 0.5% by weight). Mechanical property studies were conducted following ASTM D 882 standards, and thermal stability was characterized using thermogravimetry. The results showed an increase in elongation at break and Young's modulus percentages as the concentration of the additive increased, demonstrating its physical-chemical compatibility. Additionally, the effect on the polymer’s thermal degradation was analyzed, resulting in a directly proportional relationship between activation energy and the concentration of the material. Finally, these results demonstrate that allophane as an additive enhances the mechanical properties of recycled low-density polyethylene (12-36%) and accelerates its thermal degradation process, reducing environmental impact.

We investigate the stability of the steady-state behavior of a variant of the classic Lotka-Volterra predator-prey model. The variant, LV(3,n), involves three interacting species distributed among n patches with diffusive interaction between the patches; one of the species is allowed to migrate between adjacent patches. Criteria on the phase-space of the three interaction constants are determined to ensure stability of the population steady-states.

The purpose of this paper is to compare the coverage probability errors of the parametric bootstrap with that of the delta method for the covariance parameters of a regression model with auto-regressive fractionally integrated moving average (ARFIMA) errors. We consider the coverage probability errors of both confidence intervals (CIs) and tests based on the the plug-in Whittle maximum likelihood (PWML) estimators. We first show that, under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values, the bounds on the coverage probability errors of the two-sided delta method and parametric bootstrap confidence intervals on the plug-in Whittle likelihood estimator or the covariance parameter are shown to be $O(n^{-1})$ and $o(n^{-3/2}\ln{n})$, respectively, where n is the sample size. Next, we show that those of the one-sided parametric bootstrap confidence intervals are shown to be $O(n^{-1/2})$ and $o(n^{-1}\ln{n})$, respectively. These results show that for both one-sided and two-sided confidence intervals and tests, the bootstrap provides a significant improvement over that of the delta method.

The addition of an extra parameter to standard distributions is a common technique in statistical theory. This study introduces a new generalization of the Exponentiated Inverted Weibull distribution named alpha power exponentiated Inverted Weibull distribution (APEIW). The APEIW allows for a significant amount of versatility in modeling various data forms as it accommodates upside-down bathtubs, decreasing, and reversed-J shapes for hazard rate function. Some of the APEIW’s mathematical properties are derived in close forms. The maximum likelihood estimation technique was used for the purpose of estimation. Two real life data sets were used to show the applicability of the Alpha Power Exponentiated Inverted Weibull model over all other models considered in this study.

This article presents a mathematical model for tensor complete contraction utilizing permutation group theory. The model helps in identifying the index class that dictates the complete contraction of even-order tensors. Additionally, the concept of a complete contraction closed loop is introduced along with a method for calculating the number of completely contracted images of any even-order tensor under any λ type permutation. The model is applied to investigate the algebraic structure of global conformal invariants on three-dimensional hypersurfaces. Moreover, it is shown that the generalized Willmore functional is the sole global conformal invariant in three-dimensional hypersurfaces when the difference is a constant multiple.

In this paper we study the stabilization of a non-uniform Timoshenko beam with indefinite damping terms under boundary control and prove how the damping terms can affect the decay rate asymptotically. Using the theory of perturbed problems, we obtain the stability and establish the spectrum determined growth condition for the problem. Moreover, when the two damping terms are indefinite, we provide a condition to obtain  the exponential stability.