Delay-dependent stability criteria of delayed positive systems with uncertain control inputs: Application in mosquito-borne morbidities control

Highlights：

• In light of the comments and suggestions, we have revised the paper very carefully, and ad- dressed all the points raised by the reviewers. We hope this version can be accepted to be published in Applied Mathematics and Computations. Here are some of the highlights. In this revision, our contribution mainly falls in the application part for the considered model. Firstly, we have created a mathematical model that describes an interaction between wild mosquitoes and wolbachia infected mosquitoes. Then we tried to linearize the model and get a positive system. In order to solve and find the system stability results for our mathematical model firstly, we have constructed a delayed positive system and then extended them into delayed positive system with uncertain control. While construction, we face more difficulties in finding an appropriate approach to solve the addressed mathematical model. And also in numerical examples of application part we have 6 × 6 matrices and hence it is difficult to obtain the random values in which the system stable. Finally, to prove our model is stable by this approach, we have to show that Ω+ΩμK+ΩμΔK(t) is a metzler matrix. To get this we have to adjust the gain matrix K and the uncertain matrix ΔK(t). Further the construction of Lyapunov function for this model is very strenuous.

• Finally, we would like to take this opportunity to thank the editor and the reviewers again for their constructive comments and useful suggestions, and the time and efforts that they have spent in the review process. Without the expert comments made by the editor and the reviewers, the paper would not be of this quality.