Human papillomavirus (HPV) is a common sexually transmitted infection whose transmission and disease progression depend strongly on age and are shaped by prevention strategies such as vaccination and screening. Temporal changes in transmission conditions, contact patterns, and healthcare conditions may induce epidemiological regimes that switch over time, making it difficult to characterize long-term transmission and invasion thresholds. We study an age-structured model for HPV transmission in a randomly fluctuating epidemiological environment, where temporal variability in epidemiological conditions is represented by a finite-state continuous-time Markov chain, while vaccination is assumed to remain fixed across regimes. Each regime is governed by a deterministic age-structured system. Using semigroup methods, we characterize the invasion threshold of the randomly switching system, relate it to the reproduction numbers of the regime-specific models, and derive fast- and slow-switching limits. We further establish exponential extinction of the infected population in mean and almost surely when the random reproduction number is below one, while above the threshold we obtain instability of the linearized first-moment dynamics. Our results provide a rigorous mathematical framework for understanding HPV dynamics under temporally varying epidemiological conditions.
We establish flow invariance results for semilinear systems governed by non-Hille–Yosida operators under time-dependent closed convex constraints. A new subtangential condition is introduced, together with explicit sufficient conditions for positive invariance formulated in terms of the resolvent and the nonlinear term. The results apply to systems with non-densely defined operators and time-varying constraints, and are illustrated by applications to an age-structured predator–prey model, a biofilm model, and a class of neutral functional differential equations.
In this work, we investigate a nonlocal Fisher-KPP reaction-diffusion equation in a time-almost periodic and spatially periodic environment. We focus on the long-term behaviour of solutions of such an equation with a highly concentrated nonlocal kernel. More precisely, we define a threshold value )*, expressed in terms of upper Lyapunov exponent, and show that it determines the global dynamics of the system. In others words, if lambda(* )< 0, all positive solutions converge exponentially to 0, whereas if lambda(* )> 0 and if the kernel is sufficiently concentrated, the system admits a positive and asymptotically stable almost periodic solution. Our analysis relies on the exponential separation property and on an extension of the Smith and Waltman perturbation theorem [51].
This work is part of a sustainable development approach by promoting the use of local and bio-based raw materials such as Typha, rice husk, residues from threshing millet ears, and cassava starch. The main objective was to develop, characterize, and apply these resources in innovative solutions. A manufacturing process was developed, along with specific formulations derived from these raw materials. The characterization of the materials enabled the determination of their key properties, including bulk density, mechanical characteristics and thermal properties. Composite panels were designed and integrated into an egg incubator prototype using these local materials. The results obtained show an efficient thermal insulation with thermal conductivity panels of 0.08 W/mK and satisfactory performance in terms of egg hatching of 83
In this work, we present a mathematical model for the spread of malaria, incorporating key factors such as human populations, mosquito behavior, and the mosquitoes’ plasticity and adaptation to control measures like widespread insecticide-treated mosquito nets and indoor residual spraying. Through analysis of the model, we identify and describe the convergence and persistence properties of the solutions, leveraging a small parameter that represents the interactions between mosquitoes in relation to their activity patterns. In our analysis, we extend some ideas from the theory of uniform persistence to the case of semiflow without dissipativity.
