Influence of environmental viral load, interpersonal contact and infected rodents on Lassa fever transmission dynamics: Perspectives from fractional-order dynamic modelling

J. P. Ndenda; J. B. H. Njagarah; S. Shaw; J. P. Ndenda; J. B. H. Njagarah; S. Shaw

doi:10.3934/math.2022500

AIMS Mathematics

2022, Volume 7, Issue 5: 8975-9002. doi: 10.3934/math.2022500

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Influence of environmental viral load, interpersonal contact and infected rodents on Lassa fever transmission dynamics: Perspectives from fractional-order dynamic modelling

Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Private Bag 016, Palapye, Botswana

Received: 24 November 2021 Revised: 16 January 2022 Accepted: 27 January 2022 Published: 08 March 2022
MSC : 92B05, 34A08, 26A33

Lassa fever is a fatal zoonotic hemorrhagic disease caused by Lassa virus carried by multimammate rats, which are widely spread in West Africa. In this work, a fractional-order model for Lassa fever transmission dynamics is developed and analysed. The model involves transmissions from rodents-to-human, person-to-person, as well as from Lassa virus infested environment/surfaces. The basic properties of the model such as positivity of solutions, and local stability of the disease-free equilibrium are determined. The reproduction number, $ \mathcal{R}_0 $, of the model is determined using the next generation method and it is used to determine the suitable conditions for disease progression as well as its containment. In addition, we performed sensitivity analysis of the model parameters using the Latin Hypercube Sampling (LHS) scheme to determine the most influential processes on the disease threshold, and determined the key processes to be focused on if the infection is to be curtailed. Moreover, fixed point theory was used to prove the existence and uniqueness of non-trivial solutions of the model. We used the Adams-Bashforth Moulton method to solve the model system numerically for different orders of the fractional derivative. Our results show that using various interventions and control measures such as controlling environmental contamination, reducing rodents-to-humans transmission and interpersonal contact, can significantly help in curbing new infections. Morestill, we observe that an increase in the memory effect, i.e. dependence on future values of the model on the previous states predicts lower peak values of infection cases in the short term, but higher equilibrium values in the long term.
- fractional-order model,
- Lassa virus,
- Mastomys rats,
- environmental viral load,
- sensitivity analysis
Citation: J. P. Ndenda, J. B. H. Njagarah, S. Shaw. Influence of environmental viral load, interpersonal contact and infected rodents on Lassa fever transmission dynamics: Perspectives from fractional-order dynamic modelling[J]. AIMS Mathematics, 2022, 7(5): 8975-9002. doi: 10.3934/math.2022500

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Abstract

Lassa fever is a fatal zoonotic hemorrhagic disease caused by Lassa virus carried by multimammate rats, which are widely spread in West Africa. In this work, a fractional-order model for Lassa fever transmission dynamics is developed and analysed. The model involves transmissions from rodents-to-human, person-to-person, as well as from Lassa virus infested environment/surfaces. The basic properties of the model such as positivity of solutions, and local stability of the disease-free equilibrium are determined. The reproduction number, $ \mathcal{R}_0 $, of the model is determined using the next generation method and it is used to determine the suitable conditions for disease progression as well as its containment. In addition, we performed sensitivity analysis of the model parameters using the Latin Hypercube Sampling (LHS) scheme to determine the most influential processes on the disease threshold, and determined the key processes to be focused on if the infection is to be curtailed. Moreover, fixed point theory was used to prove the existence and uniqueness of non-trivial solutions of the model. We used the Adams-Bashforth Moulton method to solve the model system numerically for different orders of the fractional derivative. Our results show that using various interventions and control measures such as controlling environmental contamination, reducing rodents-to-humans transmission and interpersonal contact, can significantly help in curbing new infections. Morestill, we observe that an increase in the memory effect, i.e. dependence on future values of the model on the previous states predicts lower peak values of infection cases in the short term, but higher equilibrium values in the long term.

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