Mathematical Modeling and Analysis of Human-to-Human Transmitted Viral Encephalitis
Md. Saifur Rahman,
Rehena Nasrin () and
Md. Haider Ali Biswas
Additional contact information
Md. Saifur Rahman: Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
Rehena Nasrin: Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
Md. Haider Ali Biswas: Mathematics Discipline, Science Engineering and Technology School, Khulna University, Khulna 9208, Bangladesh
Mathematics, 2025, vol. 13, issue 11, 1-28
Abstract:
Encephalitis, a severe neurological condition caused by human-to-human (H2H) transmitted viruses, such as herpes simplex virus (HSV), requires a rigorous mathematical framework to understand its transmission dynamics. This study develops a nonlinear compartmental model, SEITR (Susceptible–Exposed–Infected–Treated–Recovered), to characterize the progression of viral encephalitis. The basic reproduction number (R 0 ) is derived using the next-generation matrix method, serving as a threshold parameter determining disease persistence. The local and global stability of the disease-free and endemic equilibria are established through a rigorous mathematical analysis. Additionally, a sensitivity analysis quantifies the impact of key parameters on R 0 , offering more profound insights into their mathematical significance. Numerical simulations validate the theoretical results, demonstrating the system’s dynamical behavior under varying epidemiological conditions. This study provides a mathematically rigorous approach to modeling viral encephalitis transmission, filling a gap in the literature and offering a foundation for future research in infectious disease dynamics.
Keywords: viral encephalitis; H2H transmission; mathematical modeling; stability analysis; estimation of parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:
Downloads: (external link)
https://www.mdpi.com/2227-7390/13/11/1809/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/11/1809/ (text/html)
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:11:p:1809-:d:1666965
Access Statistics for this article
Mathematics is currently edited by Ms. Emma He
More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().