Global stability for a mosquito-borne disease model with continuous-time age structure in the susceptible and relapsed host classes

Mosquito-borne infectious diseases represent a significant public health issue. Age has been identified as a key risk factor for these diseases, and another phenomenon reported is relapse, which involves the reappearance of symptoms after a symptom-free period. Recent research indicates that susceptibility to and relapse of mosquito-borne diseases are frequently age-dependent. This paper proposes a new model to better capture the dynamics of mosquito-borne diseases by integrating two age-dependent factors: chronological age and asymptomatic-infection age. Chronological age refers to the time elapsed from the date of birth of the host to the present time. On the other hand, asymptomatic infection age denotes the time elapsed since the host became asymptomatic after the primary infection. The system of integro-differential equations uses flexible, unspecified functions to represent these dependencies, assuming they are integrable. We analyzed the global stability of both the disease-free and endemic equilibrium states using the direct Lyapunov method with Volterra-type Lyapunov functionals. Additionally, the paper explores several special cases involving well-known host-vector models.