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All Journal TRANSPUBLIKA INTERNATIONAL RESEARCH IN EXACT SCIENCES (TIRES)
Oladejo, Janet Kikelomo
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Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Mathematics Physics

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MATHEMATICAL ANALYSIS OF RUBELLA DISEASE DYNAMICS: THE ROLE OF VERTICAL TRANSMISSION AND VACCINATION Adewale, Sunday Olumuyiwa; Oluyo , Temitayo Olabisi; Olaitan, Lawal Wasiu; Oladejo, Janet Kikelomo
TRANSPUBLIKA INTERNATIONAL RESEARCH IN EXACT SCIENCES Vol. 3 No. 4 (2024): OCTOBER
Publisher : Transpublika Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55047/tires.v3i4.1455

Abstract

Rubella known as German measles constitutes a significant threat to global health, as every individual in the human population is vulnerable to its highly contagious and severe effects. The risk of congenital rubella syndrome is significantly elevated when pregnant women contract the virus, transmitting it to the fetus. This research develops and examines a mathematical framework to simulate rubella's transmission patterns. The model categorizes the population into seven distinct compartments: Susceptible individuals S(t), Vaccinated individuals V(t), Persons with lifelong immunity after receiving a second vaccine dose P(t), Infected individuals I(t), Treated individuals T(t), Recovered individuals R(t). A detailed examination of the model's qualitative features is presented, the formulated model was shown to have non-negative solutions in feasible regions of human population. Furthermore, the model has a stable disease-free equilibrium if the basic reproduction number  is less than unity, unstable otherwise. Computational experiments were performed using MATLAB R2013a to examine the effects of critical parameters on rubella transmission, yielding insightful graphical representations. Simulation studies revealed that reducing contact and vertical transmission rates, while increasing recovery rates, vaccination rates (first and second doses), and maternal immunization, are vital for mitigating rubella's impact in the population.
Stability and Sensitivity Analysis of HIV/AIDS Model with Saturated Incidence Rate Odebiyi, Olusola Akintunde; Oladejo, Janet Kikelomo; Wasiu Omotayo, Salahu; Taiwo, Abiodun Adewale; Ayanrinola, Olusola Wumi
TRANSPUBLIKA INTERNATIONAL RESEARCH IN EXACT SCIENCES Vol. 4 No. 2 (2025): APRIL
Publisher : Transpublika Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55047/tires.v4i2.1650

Abstract

HIV/AIDS, an extremely harmful sexually transmitted disease, has had a significant impact on worldwide health, establishing itself as one of the most lethal epidemics ever recorded. In this study, a mathematical model is used to analyze how HIV/AIDS spreads and grows, taking into account high incidence rates. The model uses a set of typical differential equations to group people into different categories based on their health status, including those who are vulnerable, those who have been vaccinated, those who are asymptomatic, those who are symptomatic, and those who have AIDS. The effectiveness of the solution indicates that the model is clearly outlined and has important implications for epidemiology. By utilizing the next-generation matrix method, we calculated the basic reproduction number. In order to evaluate the model's stability, a comprehensive examination was conducted on both the local and global stability of both the disease-free and endemic equilibrium points. This analysis provides a comprehensive understanding of the model’s behavior, shedding light on the conditions necessary for the disease to persist or die out. Numerical simulations focusing on these key parameters demonstrate that achieving a disease-free environment is attainable, albeit requiring targeted interventions to maintain stability. This study underscores the significance of understanding saturated incidence rates in modeling HIV/AIDS transmission dynamics. The results offer important information for policymakers and public health authorities, allowing them to create successful tactics for managing the transmission of HIV/AIDS.
Co-Authors Adewale, Sunday Olumuyiwa Ayanrinola, Olusola Wumi Odebiyi, Olusola Akintunde Olaitan, Lawal Wasiu Oluyo , Temitayo Olabisi Taiwo, Abiodun Adewale Wasiu Omotayo, Salahu