Advances in Mathematical Models for Renewable Resources and Population Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 26 August 2026 | Viewed by 452

Special Issue Editor


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Guest Editor
Laboratory of Nonlinear Analysis and Applied Mathematics, Department of Mathematics, University of Tlemcen, Tlemcen 13000, Algeria
Interests: dynamical systems; population dynamics; epidemiology; ecology; fishery models

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to gather original contributions and reviews on the development and application of mathematical models to sustainable development challenges. The focus will be on both theoretical advances and practical applications, with an emphasis on renewable resource management, population dynamics, and epidemic control. This Special Issue fits within the scope of Mathematics, as it highlights both pure and applied mathematical approaches that contribute to solving real-world problems. We expect the collection to stimulate interdisciplinary exchanges between mathematicians, ecologists, epidemiologists, and engineers, fostering a broader understanding of sustainability through mathematics.

Prof. Dr. Ali Moussaoui
Guest Editor

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Keywords

  • mathematical modeling
  • sustainable development
  • renewable resources
  • fisheries management
  • population dynamics
  • epidemic modeling
  • control theory
  • optimization
  • numerical methods
  • applied mathematics

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Published Papers (1 paper)

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Research

26 pages, 1187 KB  
Article
Optimizing HPV Vaccination Strategy: An Optimal Control Problem
by Amira Bouhali, Zeineb Ounissi, Ali Moussaoui, Slimane Ben Miled and Amira Kebir
Mathematics 2026, 14(10), 1634; https://doi.org/10.3390/math14101634 - 12 May 2026
Viewed by 211
Abstract
Human papillomavirus (HPV) is one of the most widespread sexually transmitted infections globally, whose persistent infection plays a major role in causing cervical cancer. Vaccination is therefore a key prevention strategy. Using a gender-stratified dynamic transmission model tailored to a Tunisian case, we [...] Read more.
Human papillomavirus (HPV) is one of the most widespread sexually transmitted infections globally, whose persistent infection plays a major role in causing cervical cancer. Vaccination is therefore a key prevention strategy. Using a gender-stratified dynamic transmission model tailored to a Tunisian case, we investigate the impact of bivalent HPV vaccination. The proposed model accounts for partial cross-immunity and captures both direct and indirect effects of female-only vaccination. We derive the basic reproduction number and the corresponding herd immunity threshold, and a global sensitivity analysis shows that vaccine coverage, efficacy, and cross-protection are strong drivers of transmission reduction. Their combined effects on disease spread are quantified by varying these parameters across biologically relevant ranges. An optimal control problem was formulated and analyzed using Pontryagin’s Maximum Principle to minimize persistent infections and cancer cases while limiting vaccination effort. Three vaccination scenarios are compared: an ideal case with full vaccine availability and two resource-constrained cases with respective maximum coverage rates of 100% and 80%. The numerical simulations revealed that the optimal strategy under unconstrained conditions can achieve significant suppression of infection, persistence, and cancer. Under constrained effort, the optimal control still achieves substantial reductions in disease burden, with minor differences in dynamics and speed of immunity buildup. Our results highlight the effectiveness of female-only HPV vaccination in providing both direct and indirect protection. They also emphasize the importance of sustained coverage in constrained settings. Full article
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