Abstract
Visceral leishmaniasis (VL) remains a lethal parasitic disease, disproportionately affecting resource-limited regions where sustained control measures are often economically and logistically impractical. Consequently, cost-effective and sustainable strategies tailored to seasonal transmission patterns are urgently needed. Because temperature and rainfall strongly influence sandfly populations, aligning control efforts with seasonal transmission dynamics may enhance effectiveness while reducing costs. This study proposes an impulsive control strategy within a temperature- and rainfall-dependent VL transmission model to assess how strategically timed, short-term interventions optimize disease control. We examine the effects of intervention timing, frequency, and coverage for measures including sandfly breeding site elimination, insecticide spraying, and culling infected reservoir animals. Theoretical analysis shows that the disease-free periodic solution is locally asymptotically stable when the basic reproduction number ((mathscr {R}_0)) is below one, while endemic persistence occurs when (mathscr {R}_0>1). The calibrated model closely reproduced observed seasonal transmission patterns, providing a robust basis for evaluating interventions under climatic forcing. Global sensitivity analysis revealed that vector-related parameters consistently drive infection burden, while reservoir parameters show negligible effects, indicating that vector control should be prioritized over reservoir culling for cost-effective VL management. Simulations indicate that targeted interventions implemented for only a few weeks annually substantially reduce transmission. Although vector control and reservoir culling independently decrease cases, their combined application is more effective. A biannual one-week intervention reduces human cases by 95.11%, increasing to 96.6% when extended to two weeks. Initiating interventions six weeks after peak infection yields the most substantial long-term impact, achieving a 98.89% reduction at 85% coverage.
Similar content being viewed by others
Leishmaniasis
Spatiotemporal analysis of environmental factors associated with visceral leishmaniasis in northeastern Brazil, 2007–2022
Inferring the regional distribution of Visceral Leishmaniasis incidence from data at different spatial scales
Acknowledgements
We are thankful to the editors and the anonymous reviewers for the valuable suggestions to improve this paper.
Funding
This research was funded by O.R. Tambo Africa Research Chairs Initiative as supported by the Botswana International University of Science and Technology, the Ministry of Tertiary Education, Science, and Technology; the National Research Foundation of South Africa (NRF); the Department of Science and Innovation of South Africa (DSI); the International Development Research Centre of Canada (IDRC); and the Oliver and Adelaide Tambo Foundation (OATF), with grant number: (UID)136696.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix A: Mathematical interpretation of model function
Appendix A: Mathematical interpretation of model function
Sandflies thrive under warm climatic conditions, with optimal development and survival observed at temperatures ranging from 18–28° C24 and moderate monthly rainfall levels up to 120 mm32. Favorable weather enhances key sandfly activities, including host-seeking, biting, blood-feeding, and rates of development and reproduction45. Conversely, prolonged exposure to temperatures below 15° C or above 32° C adversely affects sandfly survival, leading to increased mortality24. Furthermore, because sandfly larvae develop in moist soil or organic matter, heavy rainfall can destroy breeding sites and larval habitats, thereby reducing the sandfly population. Excessive precipitation may also directly wash away adult sandflies or impede their movement.
The parameter (alpha =alpha (T)), for the bitting rate of sandfly, is defined in this study as
where W(T) accounts for the effect of temperature on a weekly average bitting rate of sandflies, and (alpha _{max }) is the maximum biting rate of the sandfly per week. Similarly, the parameters (mu _v(T, Upsilon )) and (Lambda _v(T)) are defined as
Here, H(T) and (K(Upsilon )) describe the effect of temperature and rainfall, respectively, on the weekly vector mortality rate, while M(T) accounts for the temperature-dependent weekly recruitment rate of sandflies. The modification parameters (c_1), (c_T(t)), and (c_Upsilon (t)) ensure these rates remain between 0 and 1, controlling their activation according to favorable temperature and rainfall conditions.
Unlike mosquitoes, sandflies lack an aquatic life stage and complete their entire life cycle on land. Consequently, their development and survival are strongly governed by ambient temperature. Temperature critically regulates key physiological processes, including developmental rates, reproductive cycles, and mortality34. It directly influences the duration of egg hatching, larval maturation, and adult emergence, thereby playing a pivotal role in shaping sandfly population dynamics and seasonal activity patterns33. The temperature and rainfall dependent component functions are defined as
with (omega =frac{2pi }{52}) (corresponding to a one-year period in weeks), (T_{av}) and (Upsilon _{av}) are weekly average temperature and rainfall respectively, (A_1) (A_2) are the amplitude of temperature, (B_1), (B_2), (B_3), and (B_4) are the amplitude of rainfall, (overline{T}) and (overline{Upsilon }) are temperature and rainfall values that are known to be most favorable for sandflies respectively, (phi _1) and (phi _2) are the phase shift for temperature as well as (eta _1), (eta _2) , (eta _3) and (eta _4) are the phase shift for rainfall, (omega _1), (omega _2), (omega _3) and (omega _4) are the frequencies for rainfall, (sigma) is the standard deviation from the mean temperature and (nu) is the standard deviation from the mean rainfall35 and (kappa _i: i=1, 2, 3, 4) are modification parameters.
According to24, sandfly mortality increases when temperatures exceed (32^{circ }) or drop below (15^{circ }). Thus, within the range of (15^{circ }) to (32^{circ }), the climate is favorable for sandfly reproduction and survival, whereas temperatures outside this interval accelerate their death rate. Based on this observation, we formulated the modification parameter (c_T(t)) as a function of temperature, as presented in Eq. (17) and illustrated schematically in Fig. 6(a).
Furthermore heavy rainfall can flood the sites where sandfly larvae develop, the rainy season and colder temperatures are unfavorable for sandfly populations. Intense rainfall hampers sandfly activities, including flying, biting, and developmental processes. Beyond a certain rainfall value, the rain suffocates and kills the larvae of sandflies. Considering these into account, we define a piecewise modification parameter (c_Upsilon (t)) in Eq. (3) and diagrammatically as indicated in Fig. 6(b).
Furthermore, heavy rainfall can flood the larval development sites of sandflies, making both the rainy season and colder temperatures unfavorable for sandfly populations. Intense precipitation hinders critical activities such as flight, biting, and development. Beyond a certain threshold, rainfall may also suffocate and kill sandfly larvae. Taking these factors into account, we introduce a piecewise modification parameter, (c_Upsilon (t)), defined in Eq. (3) and illustrated diagrammatically in Figs. 6(b), 19.
The plot of the modification parameters (c_T(t)) and (c_Upsilon (t)).
Substituting the estimated parameter values and simplifying gives the temperature and rainfall dependent model parameters as follows.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Reprints and permissions
About this article
Cite this article
Awoke, T.D., Kassa, S.M. & Tsidu, G.M. Impulsive intervention strategies for temperature and rainfall-dependent visceral leishmaniasis transmission dynamics.
Sci Rep (2026). https://doi.org/10.1038/s41598-026-57002-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41598-026-57002-6
Keywords
- Visceral leishmaniasis
- Impulsive control
- Climate variable-dependent VL
- Reservoir animal culling
- Vector control
Source: Ecology - nature.com
