Modeling Guinea worm disease with time delays: Threshold dynamics, treatments and sensitivity analysis in heterogeneous populations

Fawaz K. Alalhareth; Ali A. Alharbi; Mohammed H. Alharbi; Miled El Hajji; Fawaz K. Alalhareth; Ali A. Alharbi; Mohammed H. Alharbi; Miled El Hajji

doi:10.3934/math.2026458

AIMS Mathematics

2026, Volume 11, Issue 4: 11116-11153. doi: 10.3934/math.2026458

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Modeling Guinea worm disease with time delays: Threshold dynamics, treatments and sensitivity analysis in heterogeneous populations

1.
Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Saudi Arabia
2.
Science and Engineering Research Center, Najran University, Najran, Saudi Arabia
3.
Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
4.
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvédère, Tunis El Manar University, Tunisia

Received: 10 March 2026 Revised: 07 April 2026 Accepted: 15 April 2026 Published: 21 April 2026
MSC : 34D23, 92D30, 92B05, 37N25

This paper presents a mathematical investigation of Guinea worm disease (GWD) dynamics using a two-patch model that incorporates discrete delays and treatment interventions. The model accounts for two distinct host populations sharing a common water source, with dynamics described by a system of delay differential equations. We compute the basic reproduction number $ \mathcal{R}_0^d $ for both the delayed and nondelayed systems and establish threshold conditions for disease eradication and persistence. Analytical results demonstrate that the disease-free equilibrium is globally asymptotically stable (GAS) when $ \mathcal{R}_0^d \leq 1 $, while a unique endemic equilibrium exists and is globally stable when $ \mathcal{R}_0^d > 1 $. Sensitivity analysis identifies key parameters influencing disease transmission, and numerical simulations explore the impact of time delays and treatment efficacy on disease dynamics. Our findings reveal that both treatment interventions and specific time delays can significantly reduce the basic reproduction number, providing valuable insights for designing effective GWD control strategies.
- Guinea worm disease,
- delay differential equations,
- global stability,
- treatment interventions,
- sensitivity analysis,
- mathematical modeling
Citation: Fawaz K. Alalhareth, Ali A. Alharbi, Mohammed H. Alharbi, Miled El Hajji. Modeling Guinea worm disease with time delays: Threshold dynamics, treatments and sensitivity analysis in heterogeneous populations[J]. AIMS Mathematics, 2026, 11(4): 11116-11153. doi: 10.3934/math.2026458

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Abstract

This paper presents a mathematical investigation of Guinea worm disease (GWD) dynamics using a two-patch model that incorporates discrete delays and treatment interventions. The model accounts for two distinct host populations sharing a common water source, with dynamics described by a system of delay differential equations. We compute the basic reproduction number $ \mathcal{R}_0^d $ for both the delayed and nondelayed systems and establish threshold conditions for disease eradication and persistence. Analytical results demonstrate that the disease-free equilibrium is globally asymptotically stable (GAS) when $ \mathcal{R}_0^d \leq 1 $, while a unique endemic equilibrium exists and is globally stable when $ \mathcal{R}_0^d > 1 $. Sensitivity analysis identifies key parameters influencing disease transmission, and numerical simulations explore the impact of time delays and treatment efficacy on disease dynamics. Our findings reveal that both treatment interventions and specific time delays can significantly reduce the basic reproduction number, providing valuable insights for designing effective GWD control strategies.

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