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All Journal Jambura Journal of Mathematics Jurnal Diferensial
Ayoola, Rasheed Gbemisola
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Mathematics Public Health

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Mathematical Analysis of Typhoid Fever Dynamics with Age-Structured Control Measures Kolawole, Mutairu Kayode; Ayoola, Rasheed Gbemisola; Adebisi, Folasade Ajimot
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.35225

Abstract

This research develops a mathematical model to investigate the dynamics of typhoid fever by incorporating age structure, vaccination and treatment strategies. Recognizing that different age groups display varying susceptibility and contact rates, the model provides a detailed representation of transmission. The analysis is to emphasize how vaccination programs and treatment interventions, when tailored to age-specific characteristics, can significantly reduce transmission and control outbreaks. The system of nonlinear differential equations describing the disease dynamics is analyzed and solved using the homotopy perturbation method. This analytical approach allows for an approximation of solutions while capturing the nonlinear interactions within the system. Sensitivity analysis is carried out to determine the most influential parameters on disease spread, particularly those affecting the basic reproduction number. The simulations reveal that increasing vaccination coverage and treatment rates leads to a decline in typhoid fever cases across all age groups. Age-targeted interventions are shown to enhance the effectiveness of control strategies compared with uniform measures. Sensitivity analysis result further indicate that parameters such as vaccination rate, treatment efficacy and contact patterns play vital roles in disease progression and a potential for its eradication.
Mathematical Analysis and Control of Typhoid Fever Dynamics Using a SEITRB Fractional Model Kolawole, Mutairu Kayode; Ayoola, Rasheed Gbemisola; Oyalade, Abidemi Damaris; Ogunleye, Timothy A.; Ayoola, Adijat Omolara
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.24943

Abstract

The seitrb compartmental model was formulated to investigate the transmission dynamics and control of typhoid fever, incorporating the susceptible, exposed, infected, treatment, recovered, and environmental bacteria populations. The model was analyzed for well-posedness, establishing existence, uniqueness, positivity, and boundedness of solutions. Equilibrium states were examined under both disease-free and endemic conditions, with the basic reproduction number derived as the threshold parameter. The analysis showed that typhoid infection dies out when but persists when . Local and global stability analyses were established, while sensitivity analysis identified treatment rate, bacterial decay, and vaccination efficacy as the most influential parameters on . Numerical simulations, carried out using the Laplace Adomian Decomposition Method in conjunction with Caputo fractional derivatives, illustrated the impact of control measures. Findings revealed that optimal treatment effectiveness, sufficient treatment coverage, and improvements in sanitation act synergistically to minimize infection and reinfection risks. Over a multi-year horizon, these combined interventions significantly reduced disease prevalence in endemic populations. This study demonstrates that integrating mathematical analysis with practical interventions provides a robust model for understanding typhoid dynamics. By identifying the parameters most critical to disease reduction, the seitrb model offers evidence-based guidance for health practitioners in designing localized and sustainable typhoid control strategies. Overall, the model highlights the transformative role of coordinated vaccination, treatment, and sanitation in achieving effective prevention and long-term community health improvement.
Co-Authors ADEBISI, Folasade Ajimot Ayoola, Adijat Omolara Kolawole, Mutairu Kayode Ogunleye, Timothy A. Oyalade, Abidemi Damaris