Modelling the transmission dynamics of two-strain Dengue in the presence awareness and vector control

•A two-strain Dengue virus mathematical model with vector control and awareness of susceptible humans is proposed.•The sufficient conditions on the existence and stability of three equilibria states are obtained.•The persistence of disease is studied.•The sensitivity analysis of threshold conditions and the optimal control strategy for this disease are discussed.•Numerical simulations and discussions are carried out to illustrate the main results. In this paper, a mathematical model describing the transmission of two-strain Dengue virus between mosquitoes and humans, incorporating vector control and awareness of susceptible humans, is proposed. By using the next generation matrix method, we obtain the threshold values to identify the existence and stability of three equilibria states, that is, a disease-free state, a state where only one serotype is present and another state where both serotypes coexist. Further, explicit conditions determining the persistence of this disease are also obtained. In addition, we investigate the sensitivity analysis of threshold conditions and the optimal control strategy for this disease. Theoretical results and numerical simulations suggest that the measures of enhancing awareness of the infected and susceptible human self-protection should be taken and the mosquito control measure is necessary in order to prevent the transmission of Dengue virus from mosquitoes to humans.