Global stability of infectious disease models with contact rate as a function of prevalence index
Cruz Vargas-De-León Alberto d'Onofrio
Mathematical Biosciences & Engineering 2017, 14(4): 1019-1033 doi: 10.3934/mbe.2017053

In this paper, we consider a SEIR epidemiological model with information-related changes in contact patterns. One of the main features of the model is that it includes an information variable, a negative feedback on the behavior of susceptible subjects, and a function that describes the role played by the infectious size in the information dynamics. Here we focus in the case of delayed information. By using suitable assumptions, we analyze the global stability of the endemic equilibrium point and disease-free equilibrium point. Our approach is applicable to global stability of the endemic equilibrium of the previously defined SIR and SIS models with feedback on behavior of susceptible subjects.

keywords: Behavioral epidemiology information variable negative feedback Lyapunov function global stability
Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes
Cruz Vargas-De-León
Mathematical Biosciences & Engineering 2012, 9(1): 165-174 doi: 10.3934/mbe.2012.9.165
A delayed vector-bias model for malaria transmission with incubation period in mosquitoes is studied. The delay $\tau$ corresponds to the time necessary for a latently infected vector to become an infectious vector. We prove that the global stability is completely determined by the threshold parameter, $R_0(\tau)$. If $R_0(\tau)\leq1$, the disease-free equilibrium is globally asymptotically stable. If $R_0(\tau)>1$ a unique endemic equilibrium exists and is globally asymptotically stable. We apply our results to Ross-MacDonald malaria models with an incubation period (extrinsic or intrinsic).
keywords: Malaria transmission global stability time delay Lyapunov functional.

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