•  
  •  
 

Turkish Journal of Mathematics

Author ORCID Identifier

HÜSEYİN DEMIR: 0000-0003-3606-878X

İNCİ ÇİLİNGİR SÜNGÜ: 0000-0001-7788-181X

İBRAHİM KELES: 0000-0001-8252-2635

Abstract

​In this paper, we propose and analyse a delayed-compartmental mathematical model of prostate cancer dynamics that incorporates vertical transmission and therapeutic intervention. The population is stratified into five compartments: susceptible (S), infected/virally activated (I), asymptomatic infectious under treatment (A), malignant untreated (M), and recovered (R). A discrete time delay τ > 0 is introduced in the force-of-infection term to model the age-dependent onset of susceptibility in middle-aged adult males. Vertical transmission of viral etiology at a rate qΛ ensures that a fraction of newborns enter the infected compartment directly, rendering the disease persistent regardless of the basic reproduction number R₀. We rigorously establish: (i) well-posedness and positive invariance of solutions; (ii) the explicit formula R₀ = β(1−q)Λ / [μ(α+μ)]; (iii) local and global asymptotic stability of the disease-free equilibrium E₀ when R₀ < 1; (iv) existence of a unique endemic equilibrium E* that persists for all q > 0; and (v) existence of a critical delay threshold τ_c beyond which a Hopf bifurcation occurs, generating stable limit cycles. Numerical simulations using a delayed Euler scheme confirm all theoretical findings and illustrate distinct qualitative behaviours across parameter regimes.

DOI

10.55730/1300-0098.3781

Keywords

Prostate cancer model, time delay, vertical transmission, basic reproduction number, Hopf bifurcation, Lyapunov stability, DDE numerical methods

First Page

1053

Last Page

1066

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Download

Included in

Mathematics Commons

Share

COinS