Stability analysis of a model for a vector-borne disease with an asymptomatic class
Keywords:
vector-borne disease, dynamical systems, asymptotic analysis, Lyapunov stabilityAbstract
We introduce a model for a vector-borne disease with symptomatic and asymptomatic carrier classes described by a system of ordinary differential equations. We analyse the local and the global stability of the disease-free and the endemic equilibria using appropriately chosen Lyapunov functions.
References
V. Duong et al. Asymptomatic humans transmit dengue virus to mosquitoes. Proc. Natl. Acad .Sci. USA, 11 (2015). 14688–14693.
L. Esteva, C. Vargas. Analysis of a dengue disease transmission model. Math. Biosci., 150 (1998), 131–151.
C. M. Gossner, E. Ducheyne, F. Schaffner. Increased risk for autochthonous vectorborne infections transmitted by Aedes albopictus in continental Europe. Eurosurveil, 23 (2018), 1800268.
M. Johansson, P. Vasconcelos, J. Staples. The whole iceberg: estimating the incidence of yellow fever virus infection from the number of severe cases. Trans. R. Soc. Trop. Med. Hyg. 108 (2014), 482–487.
J. P. LaSalle. Some extensions of Liapunov’s second method. IRE Trans. Circuit Theory, CT7 (1960), 520–527.
G. G. Mwanga, H. Haario, V. Capasso. Optimal control problems of epidemic systems with parameter uncertainties: Application to a malaria two-age-classes transmission model with asymptomatic carriers. Math. Biosci., 261 (2015), 1–12.
N. M. Nguyen et al. Host and viral features of human dengue cases shape the population of infected and infectious Aedes aegypti mosquitoes. Proc. Natl. Acad. Sci. USA, 110 (2013), 9072–9077.
M. O. Souza. Multiscale analysis for a vector-borne epidemic model. J. Math. Biol., 68 (2014), 1269–1293.
Q. A. ten Bosch et al. Contributions from the silent majority dominate dengue virus transmission. PLoS Pathog. 14 (2018), e1006965.