Dynamics of discrete Ricker models on mosquito population suppression

Dengue fever is currently one of the most serious mosquito‐borne infectious disease in the world. How to effectively prevent the outbreak of dengue fever has become a matter of significant public health concern. In this work, the cytoplasmic incompatibility induced by Wolbachia is assumed to be complete. Based on this assumption, we establish an extended discrete Ricker model with overlapping generations to investigate the suppression of mosquito population in the wild by adopting two different release strategies: the constant release strategy and the proportional release strategy. We prove the nonnegativity, boundedness, and stability of equilibrium points and finally find the release threshold, denoted as r1∗$$ {r}_1^{\ast } $$ and k1∗$$ {k}_1^{\ast } $$, for the successful suppression in these two release strategies. In addition, we demonstrate that the model that adopts the constant release strategy, respectively, has a saddle node bifurcation when r=r1∗$$ r={r}_1^{\ast } $$ and a stable period‐doubling bifurcation when r=r2∗$$ r={r}_2^{\ast } $$. While in the case of proportional release strategy, the model exhibits a transcritical bifurcation when k=k1∗$$ k={k}_1^{\ast } $$ and a stable period‐doubling bifurcation when k=k2∗$$ k={k}_2^{\ast } $$. Finally, we substantiate the conclusions through numerical simulations.