| Citation: |
Teng-Fei Jin, Hai-Feng Huo, Shuanglin Jing, Hong Xiang. MODELING THE EFFECTS OF EXTERNAL PROTECTION MEASURES AND OPTIMAL CONTROL ON SEASONAL LASSA FEVER OUTBREAKS IN NIGERIA[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3433-3464. doi: 10.11948/20240567
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MODELING THE EFFECTS OF EXTERNAL PROTECTION MEASURES AND OPTIMAL CONTROL ON SEASONAL LASSA FEVER OUTBREAKS IN NIGERIA
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Abstract
Lassa fever, also referred to as Lassa hemorrhagic fever, is an endemic viral disease that frequently triggers epidemics in West Africa. This study presents a disease transmission dynamics model of Lassa fever that integrates external protective measures, the dynamics of rodent reproductive cycles, and the periodic nature of transmission from rodents to humans, aiming to provide a comprehensive understanding of the disease. The basic reproduction number $ \mathcal R_{0} $ can be deduced and as a threshold parameter for global dynamics. The disease-free periodic solution is globally asymptotically stable when $ \mathcal R_{0}<1 $, and the disease persists when $ \mathcal R_{0}>1 $. Based on the data provided by the Nigerian Center for Disease Control and Prevention, the Markov Chain Monte Carlo algorithm is used to simulate the model to find the baseline values of the unknown parameters and the exact value of $ \mathcal R_{0} $ is calculated as 1.6237. Next, the optimal control problem associated with the model is solved through the application of the Pontryagin maximum principle, implementing optimal control strategies for mitigating the transmission of Lassa fever virus. Finally, sensitivity analyses is conducted to determine the key parameters affecting the number of the infectious individuals. The findings suggest that enhancing the rate of external protection and optimizing protective efficiency have a substantial impact on the incidence of Lassa fever infections, serving as effective measures for disease control. However, these measures alone cannot completely eliminate disease transmission. If both measures to reduce rodent transmission and increase mortality rates are implemented, it will be possible to control the epidemic.
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Keywords:
- Lassa fever /
- external protection /
- mathematical model /
- parameter estimation /
- optimal control
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References
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Teng-Fei Jin, Hai-Feng Huo, Shuanglin Jing, Hong Xiang. MODELING THE EFFECTS OF EXTERNAL PROTECTION MEASURES AND OPTIMAL CONTROL ON SEASONAL LASSA FEVER OUTBREAKS IN NIGERIA[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3433-3464. doi: 10.11948/20240567
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Figure 1.
Flow chart of Lassa fever transmission between rodents and humans, where dashed arrows indicate the direction of transmission between humans and rodents.
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Figure 2.
Monthly number of cases of seasonal Lassa fever from March 2020 to February 2024 from Nigeria CDC.
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Figure 3.
Fitting results of Lassa fever infection cases in Nigeria.
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Figure 4.
(a) Markov chain for the last 2000 samples of
$ \mathcal R_{0} $ $ \mathcal R_{0} $ $ \mathcal R_{0} $ $ \mathcal R_{0} $ -
Figure 5.
Lassa fever will gradually disappear, when
$ \mathcal R_{0}<1 $ -
Figure 6.
The uniform persistence of Lassa fever
$ \mathcal R_{0}=1.6237>1 $ -
Figure 7.
The number of individuals infected with Lassa fever over time when a control measure
$ u_{1} $ $ u_{3} $ -
Figure 8.
(a) The number of infected individuals over time with the implementation of two control measures
$ u_{2} $ $ u_{3} $ $ u_{2} $ $ u_{3} $ $ u_{4} $ -
Figure 9.
Effect of parameter changes in the system (2.1) on new infections.
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Figure 10.
Changes over time in the number of newly infected individuals at different levels of external protection efficiency and external protection rate of susceptible individuals.