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A dengue epidemic model highlighting vertical–sexual transmission and impulsive control strategies

Abstract:

Together with emerging infectious diseases, dengue fever continues to ravage tropical and subtropical countries amidst weak health systems. Vertical and sexual transmission have been shown to exhibit synergism in the endemic maintenance during inter-epidemics. This work presents a SISUV model modulating horizontal transmission, also vertical and sexual transmission in mosquitoes. Mendel's law applied to non-genetic reproduction is the key tool in the model derivation. Our finding on time scale separation reveals that certain solution trajectories approach a slow manifold before advancing toward the critical manifold and finally confining to a stable equilibrium. Equilibria in the critical manifold disclose a supercritical bifurcation around the threshold of the basic reproductive number, where the latter is shown to exhibit high sensitivity to the vertical transmission. Further extension of the model includes seasonal effects inspired by periodically varying meteorological factors. We then study how awareness campaigns and pesticide spraying contribute to compromising the disease spread, brought within toward-realistic impulsive mechanisms. The final format of the model is then numerically analyzed via path-following methods for hybrid dynamical systems, which allows to gain deeper insight into the effect of key model parameters on the system behavior. Furthermore, the proposed control scheme is optimized for efficient use of limited resources, in terms of reduction of the dengue spread among the population.