Modelling the impact of dynamic hygiene behaviour on typhoid transmission dynamics with antibiotic resistance

Maria M. Shaale; Josiah Mushanyu; Farai Nyabadza; Samuel M. Nuugulu; Maria M. Shaale; Josiah Mushanyu; Farai Nyabadza; Samuel M. Nuugulu

doi:10.3934/mbe.2026102

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 9: 2904-2941. doi: 10.3934/mbe.2026102

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Modelling the impact of dynamic hygiene behaviour on typhoid transmission dynamics with antibiotic resistance

1.
Department of Computing, Mathematical & Statistical Science, University of Namibia, Windhoek 13301, Namibia
2.
Department of Geosciences, University of Namibia, Keetmanshoop, Namibia
3.
Department of Mathematics & Applied Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
4.
Institute of Research and Professional Training, Emirates Aviation University, Dubai International Academic City, UAE

Received: 28 March 2026 Revised: 30 May 2026 Accepted: 03 June 2026 Published: 22 September 2026

In this paper, we develop a mathematical model to investigate the impact of dynamic hygiene behaviour on the transmission dynamics of typhoid fever in the presence of antibiotic resistance. The model extends existing modelling approaches by integrating behavioural responses with treatment and resistance dynamics. The model is calibrated using cumulative data on typhoid cases reported at the Mbandjock District Hospital in Cameroon. The calibrated parameter estimates give $ \mathcal{R}_0 = 2.0754 > 1 $ and $ \mathcal{R}_{0e} = 1.9509 > 1 $. These values indicate that the disease can persist in the population and remains endemic in the region. A sensitivity analysis of the basic reproduction number is performed to identify the parameters that have the greatest influence on disease transmission. The results show that the environmental transmission rate $ \beta_b $ and the bacterial decay rate $ \mu_b $ in the environment are among the most influential parameters affecting the value of $ \mathcal{R}_0 $. The model shows the possibility of backward bifurcation, indicating that reducing the reproduction number below one may not be enough to eliminate the disease, particularly in settings with poor hygiene or high levels of antibiotic resistance. Numerical simulations demonstrate that improved hygiene practices can significantly reduce infections and environmental contamination. In general, the findings show the importance of combining behavioural interventions with effective treatment strategies to control typhoid fever.
- typhoid fever,
- antibiotic resistance,
- dynamic hygiene behaviour,
- bifurcation analysis,
- mathematical modelling
Citation: Maria M. Shaale, Josiah Mushanyu, Farai Nyabadza, Samuel M. Nuugulu. Modelling the impact of dynamic hygiene behaviour on typhoid transmission dynamics with antibiotic resistance[J]. Mathematical Biosciences and Engineering, 2026, 23(9): 2904-2941. doi: 10.3934/mbe.2026102

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Abstract

In this paper, we develop a mathematical model to investigate the impact of dynamic hygiene behaviour on the transmission dynamics of typhoid fever in the presence of antibiotic resistance. The model extends existing modelling approaches by integrating behavioural responses with treatment and resistance dynamics. The model is calibrated using cumulative data on typhoid cases reported at the Mbandjock District Hospital in Cameroon. The calibrated parameter estimates give $ \mathcal{R}_0 = 2.0754 > 1 $ and $ \mathcal{R}_{0e} = 1.9509 > 1 $. These values indicate that the disease can persist in the population and remains endemic in the region. A sensitivity analysis of the basic reproduction number is performed to identify the parameters that have the greatest influence on disease transmission. The results show that the environmental transmission rate $ \beta_b $ and the bacterial decay rate $ \mu_b $ in the environment are among the most influential parameters affecting the value of $ \mathcal{R}_0 $. The model shows the possibility of backward bifurcation, indicating that reducing the reproduction number below one may not be enough to eliminate the disease, particularly in settings with poor hygiene or high levels of antibiotic resistance. Numerical simulations demonstrate that improved hygiene practices can significantly reduce infections and environmental contamination. In general, the findings show the importance of combining behavioural interventions with effective treatment strategies to control typhoid fever.

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