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The introduction of endosymbiont Wolbachia into laboratory-reared mosquito populations, which are then released to mix with natural populations to prevent the mosquito vectors from reproducing and thus break the transmission cycle of dengue disease, is an innovative new technology. Field trials of Wolbachia -carrying mosquitoes have now been implemented in many countries where there have been the outbreaks of dengue disease. A mathematical model is proposed to investigate the effects of non-identical sex ratio releases of Wolbachia -carrying mosquitoes on the control of dengue transmission. Firstly, we analyzed the existence and stability of equilibria for the system and proved the existence of forward and backward bifurcations. Secondly, bifurcation diagrams, the basins of attraction of the equilibria and the effects of mosquito augmentation for the system with imperfect and perfect transmission rates were obtained. Thirdly, three possible results for mosquito augmentation were summarized for different parameter regions. Further we explored an uncertainty and sensitivity analysis of solutions to estimate the effects of different parameter values on the success or failure of population replacement. Based on the above analysis, we considered a series of relevant issues such as (a) whether or not mosquito augmentation can ensure the success of population replacement? (b) If not, what are the parameter regions for the success or possible success of population replacement? (c) How does the initial density of natural mosquitoes and the quantity of mosquito augmentations affect the success of population replacement? (d) Whether all population replacements are effective for reducing the spread of dengue virus in the end? The results of this study will be helpful for public health authorities in designing proper strategies of mosquito augmentations for the control of dengue disease. [ABSTRACT FROM AUTHOR]

The infected population triggered threshold policy has been widely used in the prevention and control of infectious diseases. This study proposes a Filippov model with nonlinear threshold function and saturated treatment function to describe the newly infected population triggered control strategy and medical resource constraints. The existence conditions for sliding segments, sliding dynamics and different type of equilibria are derived and the local and global discontinuity-induced bifurcations including the boundary equilibrium bifurcation, tangency bifurcation and limit cycle bifurcations are theoretically and numerically analyzed. Particularly, both persistence and non-smooth fold can be observed in the boundary equilibrium bifurcations. The results show that the proposed model may have multiple sliding segments, which is caused by the nonlinear threshold function. Numerical analysis shows that when there is an unstable focus for the control system, a homoclinic loop with a boundary saddle may occur along with the boundary saddle bifurcation, and then it becomes a sliding limit cycle. This is a novel phenomenon. The numerical global behavior analysis reveals that the threshold control policy has no advantage if the newly infected population threshold is above the equilibrium level of the free system. However, if the threshold level is preset too low, a worse case may occur, in which the (newly) infected population fluctuate in a large range and the peak exceeds the equilibrium level of the free system. Thus our results suggest that suitable threshold level should be carefully chosen so that the ideal attractor with a low number or a small range of fluctuations of (newly) infected individuals is approximated. • A novel Filippov epidemic model with newly infected population triggered threshold control policy and medical-resource constraints is proposed. • Multiple sliding segments and a homoclinic loop with a boundary saddle exist due to the nonlinear threshold function. • Both persistence and non-smooth fold could be observed in the boundary equilibrium bifurcations. • The threshold control policy has no advantage if the newly infected population threshold is above the equilibrium level of the free system. • Lower threshold level does not mean better control effect. [ABSTRACT FROM AUTHOR]