Age Structured Epidemic Model under Vaccination with Vector Transmission
Dengue remains a major global public health concern due to its high mortality and economic burden. Mathematical modeling is essential to understand its transmission mechanisms and for evaluating intervention strategies. In this paper, we formulate a vector host model in which the human population is structured by age, and vaccinated individuals are further described by time since vaccination. The mosquito population is coupled to the host dynamics and reduced under a quasi steady state assumption. By integrating over vaccination age, we obtain a nonlinear steady state formulation and express the endemic equilibrium as a fixed point problem for the infected mosquito population. Using Lipschitz estimates and a contraction argument, we establish existence and uniqueness of the equilibrium under a weak transmission condition. The analysis highlights the influence of age dependent vaccination on long term dengue dynamics.