Abstract
Asymptomatic transmission is a way of spreading malaria from asymptomatic infected individuals to susceptible ones by mosquito bites. Asymptomatic malaria-infected individuals do not show clinical symptoms, but they can still transmit the disease. Motivated by mathematical models with asymptomatic infections, we propose a human–mosquito model for malaria transmission dynamics with asymptomatic infections and standard incidence rates. We calculate the basic reproduction number R0 of the model and then prove that the model exists a unique endemic equilibrium E∗ if and only if R0>1. By the Lyapunov function method, the global stability of equilibria of the model is obtained. It is shown that the disease-free equilibrium E0 is globally asymptotically stable (GAS) if and only if R0≤1, which implies that malaria will be extinct; and the endemic equilibrium E∗ is GAS if and only if R0>1, which suggests that malaria will persist. In addition, the effects of partial malaria-related parameters on the dynamic transmission of malaria are studied and analysed numerically. The results of numerical simulations show that asymptomatic infections can shift the epidemic dynamics of malaria and have a significant influence on the transmission of malaria.
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