Mathematical Modeling in Epidemiology and Dynamical Systems Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E3: Mathematical Biology".

Deadline for manuscript submissions: closed (20 April 2025) | Viewed by 587

Special Issue Editor


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Guest Editor
Department of Mathematics and Applications, University of Naples Federico II, Naples, Italy
Interests: dynamical systems; mathematical epidemiology; mathematical ecology; optimal control; agent-based models; kinetic models

Special Issue Information

Dear Colleagues,

The research on the modeling of the spread of infectious diseases, which had already been in rapid evolution in the pre-COVID era, has received a major impetus by the recent pandemic. In this discipline, various degrees of complexity synergistically interplay so that broad and differentiated expertise is required.

On one hand, mathematical epidemiology had an important theoretical value per se, by bringing advances to various areas of the dynamical systems theory and mathematical analysis. On the other hand, it contributed to the understanding of the spread and control of infectious diseases by also assisting public health decisions and policies.

Nonetheless, there are still many challenges to face. In modern societies, where information is rapidly disseminated and filtered by social media, the dynamics of an infectious disease are much more complex than in the past. This requires the investigations of new mathematical approaches that are able to capture the link between the disease spread and the social structure of the host population, including human behaviour and mobility patterns.

This Special Issue aims to collect papers that introduce novel mathematical approaches to unravel the link between social and epidemiological phenomena. Papers that also provide new insights in the dynamical systems theory are particularly encouraged.

Dr. Rossella Della Marca
Guest Editor

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Keywords

  • epidemic models
  • qualitative analysis
  • social phenomena
  • human behaviour

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Published Papers (1 paper)

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Research

31 pages, 1280 KiB  
Article
Effective Control Strategies for Sex-Structured Transmission Dynamics of Visceral Leishmaniasis
by Temesgen Debas Awoke, Semu Mitiku Kassa, Kgomotso Susan Morupisi and Gizaw Mengistu Tsidu
Mathematics 2025, 13(12), 1929; https://doi.org/10.3390/math13121929 - 10 Jun 2025
Viewed by 316
Abstract
Visceral leishmaniasis (VL), a chronic disease caused by Leishmania infantum, is more prevalent in males than females. Control strategies that do not take this disparity into account can be suboptimal. We extended a sex-structured VL model by introducing four control variables: insecticide-treated bed [...] Read more.
Visceral leishmaniasis (VL), a chronic disease caused by Leishmania infantum, is more prevalent in males than females. Control strategies that do not take this disparity into account can be suboptimal. We extended a sex-structured VL model by introducing four control variables: insecticide-treated bed nets, vector control, medical treatment, and animal culling. The study evaluates six intervention strategies and calculates the incremental cost-effectiveness ratio to assess their impact on disease transmission and cost-effectiveness. The analysis shows that, without interventions, the disease remains endemic with significant health and socioeconomic consequences. The proposed strategy, which applies all four controls, emerges as the most effective and cost-efficient strategy, leading to an exponential reduction in disease prevalence across human, vector, and animal populations. Strategies without animal culling and vector control followed in effectiveness. Moreover, it was found that applying up to 50% of the controls to females, compared to males, can still eliminate VL within the planning period. Full article
(This article belongs to the Special Issue Mathematical Modeling in Epidemiology and Dynamical Systems Theory)
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