Memory-driven fractional dynamics of Pneumonia transmission with prophylactic intervention

Document Type : Research Article

Authors

Kaushal Soni ¹

Sanjeev Kumar ²

Shyamsunder Kumawat ³

Arvind Kumar Sinha ¹

¹ Department of Mathematics, National Institute of Technology Raipur, India.

² Department of Mathematics, Khandari Campus, Agra, India., Maharaja Suhel Dev University Azamgarh India.

³ Department of Mathematics, SRM University Delhi-NCR, Sonepat, Haryana, India.

10.22067/ijnao.2026.97941.1852

Abstract

‎ A novel fractional-order mathematical model is proposed to investigate the transmission dynamics of Pneumocystis pneumonia in an immunocompromised population‎. ‎Long-term chemoprophylaxis is represented as an imperfect vaccination strategy within a Susceptible–Vaccinated–Infected framework‎. ‎The model is formulated using the Atangana–Baleanu fractional derivative in Caputo sense to incorporate memory and hereditary effects in disease transmission‎. ‎The positivity‎, ‎boundedness‎, ‎existence‎, ‎uniqueness‎, ‎and Ulam–Hyers stability of the proposed system are established‎. ‎The basic reproduction number $(\mf{R}_0)$ is derived using the next-generation matrix approach‎, ‎and the local asymptotic stability of the disease-free and endemic equilibrium points is investigated‎. ‎A numerical scheme based on Lagrange interpolation is employed to obtain approximate solutions‎. ‎Sensitivity analysis is performed to identify the parameters that most strongly influence disease transmission‎. ‎The results indicate that increasing prophylaxis coverage and efficacy substantially reduces the basic reproduction number and suppresses disease spread‎. ‎The proposed fractional-order framework provides a realistic description of pneumonia dynamics by incorporating memory effects and offers useful insights for evaluating prophylactic intervention strategies in vulnerable populations‎.

Keywords

Pneumonia transmission

Fractional-order model

Prophylaxis Imperfect vaccine

Mathematical epidemiology

Stability analysis

Subjects

• Modeling and Simulation

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