Unravelling the dynamics of Lassa fever transmission with differential infectivity: Modeling analysis and control strategies

Salihu S. Musa; Abdullahi Yusuf; Emmanuel A. Bakare; Zainab U. Abdullahi; Lukman Adamu; Umar T. Mustapha; Daihai He; Salihu S. Musa; Abdullahi Yusuf; Emmanuel A. Bakare; Zainab U. Abdullahi; Lukman Adamu; Umar T. Mustapha; Daihai He

doi:10.3934/mbe.2022613

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 13114-13136. doi: 10.3934/mbe.2022613

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Unravelling the dynamics of Lassa fever transmission with differential infectivity: Modeling analysis and control strategies

1.
Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
2.
Department of Mathematics, Kano University of Science and Technology, Wudil, Kano, Nigeria
3.
Department of Computer Engineering, Biruni University, Istanbul, Turkey
4.
Department of Mathematics, Federal University Oye Ekiti, Ekiti, Nigeria
5.
Biomathematics and Applied Mathematical Modelling Research Group, Federal University Oye Ekiti, Ekiti, Nigeria
6.
Department of Biological Sciences, Federal University Dutsin-Ma, Katsina, Nigeria
7.
Department of Mathematical Sciences, Faculty of Science, University of Maiduguri, Nigeria
8.
Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria

Academic Editor: Xiaodi Li

Received: 30 May 2022 Revised: 23 August 2022 Accepted: 28 August 2022 Published: 06 September 2022

Epidemic models have been broadly used to comprehend the dynamic behaviour of emerging and re-emerging infectious diseases, predict future trends, and assess intervention strategies. The symptomatic and asymptomatic features and environmental factors for Lassa fever (LF) transmission illustrate the need for sophisticated epidemic models to capture more vital dynamics and forecast trends of LF outbreaks within countries or sub-regions on various geographic scales. This study proposes a dynamic model to examine the transmission of LF infection, a deadly disease transmitted mainly by rodents through environment. We extend prior LF models by including an infectious stage to mild and severe as well as incorporating environmental contributions from infected humans and rodents. For model calibration and prediction, we show that the model fits well with the LF scenario in Nigeria and yields remarkable prediction results. Rigorous mathematical computation divulges that the model comprises two equilibria. That is disease-free equilibrium, which is locally-asymptotically stable (LAS) when the basic reproduction number, $ {\mathcal{R}}_{0} $, is $ < 1 $; and endemic equilibrium, which is globally-asymptotically stable (GAS) when $ {\mathcal{R}}_{0} $ is $ > 1 $. We use time-dependent control strategy by employing Pontryagin's Maximum Principle to derive conditions for optimal LF control. Furthermore, a partial rank correlation coefficient is adopted for the sensitivity analysis to obtain the model's top rank parameters requiring precise attention for efficacious LF prevention and control.
- Lassa fever,
- epidemic,
- modeling,
- reproduction number,
- stability,
- optimal control
Citation: Salihu S. Musa, Abdullahi Yusuf, Emmanuel A. Bakare, Zainab U. Abdullahi, Lukman Adamu, Umar T. Mustapha, Daihai He. Unravelling the dynamics of Lassa fever transmission with differential infectivity: Modeling analysis and control strategies[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 13114-13136. doi: 10.3934/mbe.2022613

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Abstract

Epidemic models have been broadly used to comprehend the dynamic behaviour of emerging and re-emerging infectious diseases, predict future trends, and assess intervention strategies. The symptomatic and asymptomatic features and environmental factors for Lassa fever (LF) transmission illustrate the need for sophisticated epidemic models to capture more vital dynamics and forecast trends of LF outbreaks within countries or sub-regions on various geographic scales. This study proposes a dynamic model to examine the transmission of LF infection, a deadly disease transmitted mainly by rodents through environment. We extend prior LF models by including an infectious stage to mild and severe as well as incorporating environmental contributions from infected humans and rodents. For model calibration and prediction, we show that the model fits well with the LF scenario in Nigeria and yields remarkable prediction results. Rigorous mathematical computation divulges that the model comprises two equilibria. That is disease-free equilibrium, which is locally-asymptotically stable (LAS) when the basic reproduction number, $ {\mathcal{R}}_{0} $, is $ < 1 $; and endemic equilibrium, which is globally-asymptotically stable (GAS) when $ {\mathcal{R}}_{0} $ is $ > 1 $. We use time-dependent control strategy by employing Pontryagin's Maximum Principle to derive conditions for optimal LF control. Furthermore, a partial rank correlation coefficient is adopted for the sensitivity analysis to obtain the model's top rank parameters requiring precise attention for efficacious LF prevention and control.

References

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