Abstract
In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The reproductive number R0 is derived. By using the method of Lyapunov function, the global dynamics of the PDE model is further established, and the results show that the basic reproduction number R0 determines the transmission dynamics of vector-borne diseases: the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1, and the endemic equilibrium is globally asymptotically stable if R0 > 1. The results suggest that an effective strategy to contain vector-borne diseases is decreasing the basic reproduction number R0 below one.
Highlights
Vector-borne diseases are infectious diseases caused by pathogens and parasites in human populations that are transmitted to people by blood-sucking arthropods, such as mosquitoes, ticks and fleas
We develop an age-structured model to study how transmission dynamics of the vector-borne diseases are affected by the incubation and infectious ages
By using a class of global Lyapunov functions we show that the global dynamics of the system is completely determined by the basic reproduction number R0: if R0 < 1 the disease-free equilibrium is globally asymptotically stable; if R0 > 1, a unique endemic equilibrium is globally asymptotically stable
Summary
Vector-borne diseases are infectious diseases caused by pathogens and parasites in human populations that are transmitted to people by blood-sucking arthropods, such as mosquitoes, ticks and fleas. We develop an age-structured model to study how transmission dynamics of the vector-borne diseases are affected by the incubation and infectious ages. Lyapunov function has been used to study the global stability of epidemic models with age of infection [28, 29, 30]. We use Lyapunov functions to study the global dynamics of a vector-borne disease model with incubation age of the exposed hosts and infection age of the infectious hosts. We formulate a vector-borne epidemic model with incubation age of exposed hosts and infection age of infectious hosts. We study the following infection-age-structured mosquito-borne model of Dengue virus.
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