Dynamic Models of the Infection of Lassa Fever Epidemics Incorporating Detected and Undetected Class
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153-180
Digital Object Identifier:
10.58578/ajstea.v3i1.4841
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Authors:
Hamisu Idi1, Kazeem E. Lasisi2, M. Abdulhameed3, A. M. Kwami4, Muhammad Mubarak Muhammad5* 
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Abstract
In the scope of this research endeavor, we embarked on the development of a dynamic model, intricately designed to scrutinize the intricate dynamics of Lassa fever transmission, encompassing both detected and undetected cases. Our central objective revolved around the meticulous examination of how a vaccine could exert its influence on the transmission dynamics of Lassa disease. The study encompassed an exhaustive exploration of the model's equilibrium states, diligently scrutinizing both disease-free and endemic equilibria. To shed light on the potential for disease spread, we calculated the pivotal epidemiological parameter, the basic reproduction number, employing the rigorous next-generation matrix methodology. Subsequently, we delved into a comprehensive stability analysis, encompassing both local and global stability assessments. The Routh-Hurwitz conditions were harnessed for local stability analysis, while the Castillo-Chavez criterion was leveraged for global stability analysis. In our quest for a profound understanding, we ventured into analytical techniques to derive exact solutions for the model, coupled with numerical computations facilitated by the versatile MATHEMATICA software. The culmination of our endeavors unveiled a compelling insight: the disease-free equilibrium attains local asymptotic stability if and only if the basic reproduction number assumes a value below unity; conversely, it stands as unstable when this threshold is exceeded. In essence, this implies that the complete eradication of Lassa fever is within reach when the secondary infection rate remains constrained below a critical threshold.
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