10.1007/s40096-023-00517-0

Deterministic modelling of optimal control strategies for dengue fever transmission in two interconnected patches

  • Afeez Abidemi*1,
  • Nur Arina Bazilah Aziz2,
  • Edson Pindza3,
  1. Department of Mathematical Sciences, Federal University of Technology Akure, Akure, Ondo State, NG
  2. Department of Mathematical Sciences, Universiti Teknologi Malaysia, Johor Bahru, Johor, 81310, MY
  3. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, ZA

Published 2023-05-29

How to Cite

Abidemi, A., Aziz, N. A. B., & Pindza, E. (2023). Deterministic modelling of optimal control strategies for dengue fever transmission in two interconnected patches. Mathematical Sciences, 18(4 (December 2024). https://doi.org/10.1007/s40096-023-00517-0
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Abstract

Abstract This paper presents a two-patch model that governs a non-autonomous system of ordinary differential equations including patch-specific insecticides (larvicide and adulticide) vector and human personal protection controls and effect of human movement to describe dengue fever transmission dynamics between the interacting human and mosquito populations of two connected patches. Next generation matrix method is used to compute the basic reproduction number ( R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_0$$\end{document} ) associated with the autonomous version of the model. Analysis of the model reveals that the model has exactly two disease-free equilibrium, namely, trivial equilibrium and biologically realistic disease-free equilibrium (BRDFE). It is shown that BRDFE is both locally and globally asymptotically stable when R0<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_0<1$$\end{document} , and unstable otherwise. The model is validated, with the aid of single-patch version of the model, using the real epidemic data related to the 2011–2012 dengue outbreaks in Selangor and Johor, Malaysia. Using optimal control approach, the non-autonomous system is analysed to estimate the effects of patch-specific time-dependent larvicide, adulticide and personal protection controls through simulations. By patch-specific time-dependent controls, we mean time-dependent controls implemented with a view to reducing dengue prevalence at the targeted patch (or location). It is shown that the implementation of combined efforts of the three control strategies simultaneously helps in curtailing dengue fever spread in both patches.

Keywords

  • Basic reproduction number,
  • Dengue fever,
  • Optimal control,
  • Stability analysis,
  • Two-patch dengue model

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