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All Journal Asian Journal of Science, Technology, Engineering, and Art Mikailalsys Journal of Mathematics and Statistics
Lasisi, Kazeem E.
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Arts Computer Science & IT Engineering Mathematics Mechanical Engineering Social Sciences

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Dynamic Models of the Infection of Lassa Fever Epidemics Incorporating Detected and Undetected Class Idi, Hamisu; Lasisi, Kazeem E.; Abdulhameed, M.; Kwami, A. M.; Muhammad, Muhammad Mubarak
Asian Journal of Science, Technology, Engineering, and Art Vol 3 No 1 (2025): Asian Journal of Science, Technology, Engineering, and Art
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ajstea.v3i1.4841

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.
On the Comparison of PAR, DARMA, and INAR in Modeling Count Time Series Data Buba, Haruna; Abdulkadir, Ahmed; Lasisi, Kazeem E.; Bishir, A.; Mashat, Strong Yusuf
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6312

Abstract

This study evaluates the forecasting and fitting performance of three advanced models—Poisson Autoregressive (PAR), Discrete Autoregressive Moving Average (DARMA), and Integer-Valued Autoregressive (INAR) for count time series data exhibiting complex features such as autocorrelation, overdispersion, and zero inflation. Both simulated and empirical datasets were analyzed, and model performance was assessed using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). The results indicate that PAR models significantly outperform DARMA and INAR models, achieving substantially lower AIC (482.53 vs. >5,310,479) and RMSE (3,742 vs. 246,682), highlighting their robustness in handling periodic trends and autocorrelation. In contrast, standard Poisson regression performs poorly under overdispersion, with an AIC approaching 5.3 million, while zero-inflated datasets compromise error metrics such as MAPE due to division by zero. Although DARMA and INAR models perform comparably, they are less effective in capturing extreme fluctuations or sudden spikes. These findings emphasize the limitations of conventional models and point to the need for more flexible approaches, such as hybrid ZIP-INAR models or Bayesian methods, to effectively manage overdispersion and zero inflation. The study concludes with a practical recommendation to prioritize PAR models when modeling autocorrelated count data.
Co-Authors Abdulhameed, M. Abdulkadir, Ahmed Bishir, A. Buba, Haruna Idi, Hamisu Kwami, A. M. Mashat, Strong Yusuf Muhammad, Muhammad Mubarak