https://doi.org/10.1140/epjp/s13360-026-07287-3
Regular Article
Exploring the dynamics of a fractional vector-host susceptible-infected and susceptible-infected-recovered models in dengue transmission
1
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
2
Department of Anatomy and Physiology, College of Medicine, Imam Mohammad Ibn Saud Islamic University (IMSIU), 13317, Riyadh, Saudi Arabia
3
Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
18
November
2025
Accepted:
29
December
2025
Published online:
19
January
2026
Abstract
Dengue fever continues to pose a serious and persistent threat to public health and remains endemic in more than fifty countries worldwide. The disease is primarily transmitted to humans through the bite of infected Aedes mosquitoes, whose wide geographic distribution, adaptation to urban settings, and sensitivity to climatic variability contribute to sustained outbreaks. Although several prevention measures (such as vector control, environmental management, and community awareness) are widely implemented, dengue transmission remains difficult to suppress due to complex human-vector interactions, heterogeneous exposure, and limitations in controlling mosquito breeding habitats. For these reasons, epidemiological and mathematical modeling has become an essential tool for systematically describing transmission mechanisms, identifying dominant risk determinants, and assessing the expected impact of intervention strategies, thereby supporting evidence-based planning for prevention and control. In this work, we formulate a host-vector mathematical model for dengue virus transmission by coupling a mosquito Susceptible-Infected (SI) subsystem with a human Susceptible-Infected-Recovered (SIR) subsystem. The model captures the exchange of infection between vector and human populations and enables a quantitative investigation of threshold dynamics. In particular, the basic reproduction number 
is derived using the next-generation matrix technique, providing a key threshold quantity that characterizes whether an initial infection can invade the population. We then analyze the stability properties of the equilibria: the local stability analysis shows that the disease-free equilibrium is asymptotically stable when 
, implying eventual elimination of dengue, whereas dengue persists and an endemic equilibrium may arise when 
. Furthermore, global stability results are established using a suitable Lyapunov function, which strengthens the conclusions beyond local behavior. To validate the theoretical outcomes and to explore the effect of the principal parameters that promote or mitigate dengue spread, numerical simulations are carried out in MATLAB for the relevant compartments. These simulations illustrate the temporal evolution of the human and mosquito populations under different epidemiological scenarios and parameter settings. In addition, sensitivity analysis is performed to quantify how variations in model parameters influence and the overall transmission dynamics. This analysis highlights the most influential factors and provides insight into which control measures (e.g., reducing mosquito biting rate, lowering vector density, or increasing recovery) may be most effective for limiting dengue transmission.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
