Abstract
In this paper, we propose a model of transmission of arboviruses, which take into account a future vaccination strategy in human population. A qualitative analysis based on stability and bifurcation theory reveals that the phenomenon of backward bifurcation may occur; the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. We show that the backward bifurcation phenomenon is caused by the arbovirus induced mortality in humans. Using theВ direct Lyapunov method, we show the global stability of the trivial equilibrium. Through global sensitivity analysis, wedetermine the relative importance of model parameters for disease transmission. Simulation results using a qualitatively stable numerical scheme, are provide to illustrate the impact of vaccination strategy in human community.
Highlights
Arboviral diseases are affections transmitted by hematophagous arthropods
Depending of the values of these thresholds, we identify two disease–free equilibria: the trivial equilibrium which corresponds to the extinction of vectors, when N ≤ 1, and the disease-free equilibrium (DFE) when N > 1 and R0 < 1
The local stability of the trivial equilibrium and the disease–free equilibrium is given in the following result: Proposition 3.2: a) If N ≤ 1, the trivial equilibrium TE is locally asymptotically stable. b) If N > 1, the trivial equilibrium is unstable and the Disease Free Equilibrium P1 is locally asymptotically stable if R0 < 1 and unstable if R0 > 1, where R0 is the basic reproduction number [26], [82], given by βhvβvhKθ(πξ + μh)(k3ηh + γh)(μh + γh)(μh + δ + σ)
Summary
Arboviral diseases are affections transmitted by hematophagous arthropods. There are currently 534 viruses registered in the International Catalogue of Arboviruses and 25% of them have caused documented illness in humans [20], [49], [42]. This said, the compartments in which the populations are divided are the following ones: –For humans, we consider susceptible (denoted by Sh), vaccinated (Vh), exposed (Eh), infectious (Ih) and resistant or immune (Rh). It is worth emphasizing that, unlike many of the published modelling studies on dengue transmission dynamics, we assume in this study that exposed vectors can transmit dengue disease to humans. This is in line with some studies
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