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All Journal Mikailalsys Journal of Mathematics and Statistics
Odebiyi, O. A.
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Engineering Mathematics Mechanical Engineering

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Mathematical Modeling of HIV Investigating the Effect of Inconsistent Treatment with Saturated Incidence Function Odebiyi, O. A.; O, Salahu W.; Oladejo, J. K.; Olabisi, O. O
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 2 (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.v3i2.5570

Abstract

The Human Immunodeficiency Virus (HIV) remains a significant global health challenge, with millions of people worldwide living with the virus. Despite advances in treatment and prevention, the disease continues to spread, underscoring the need for a deeper understanding of its transmission dynamics. This study presents a mathematical model of HIV transmission dynamics, incorporating a saturation term to capture the complex interactions among susceptible, infected, AIDS, and treated populations. The validity of the solution confirms that the model is well-defined and holds epidemiological significance. The basic reproduction number is obtained using the next-generation matrix approach. To assess the stability of the model, we conducted a thorough analysis of the local and global stability of both the disease-free and endemic equilibria. This analysis provides a comprehensive understanding of the model’s behavior, illuminating the conditions necessary for the disease to persist or die out. A sensitivity analysis is conducted to identify key parameters influencing the model’s behavior. Numerical simulations are then performed to further explore the dynamics of the system. Our results highlight the importance of targeted interventions to control the spread of the disease, thereby informing public health policy and intervention strategies.
Modelling Measles Reoccurrence in Vaccinated Infants Adeboye, O. A.; Adewale, S. O.; Odebiyi, O. A.; Oladejo, J. K.
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.v3i3.6537

Abstract

Measles is a highly contagious viral disease caused by the morbillivirus, marked by symptoms including fever, cough, runny nose, conjunctivitis, and a characteristic widespread rash. In severe cases, especially among young children and pregnant women, it can lead to complications such as ear infections, pneumonia, encephalitis, and death. This study develops a six-compartment deterministic mathematical model, expressed as a system of ordinary differential equations, to investigate the transmission dynamics of measles in human populations. The model was demonstrated to be both mathematically and epidemiologically well-posed. The basic reproduction number (R₀) was derived, and the stability analysis of the disease-free equilibrium showed it to be locally and globally asymptotically stable when R₀ < 1, and unstable when R₀ > 1. Sensitivity analysis using normalized forward sensitivity indices revealed the impact of various parameters on R₀. Specifically, parameters with negative indices, such as the vaccination rate and treatment rate reduce R₀ when increased, while those with positive indices, such as the effective contact rate increase R₀ when increased. These findings underscore the importance of increasing vaccination coverage, enhancing treatment efforts, and isolating infected individuals to control and prevent measles outbreaks. The model provides a theoretical framework for designing effective public health strategies to minimize the disease burden in the population.
Co-Authors Adeboye, O. A. Adewale, S. O. O, Salahu W. Olabisi, O. O Oladejo, J. K.