Competitive exclusion in a multi-strain malaria transmission model with incubation period

•A multi-strain malaria dynamical model with incubation period is proposed.•Global stability of the disease-free equilibrium, the existence and stability of dominant equilibria are obtained.•The existence of competitive exclusion is in-depth studied by numerical simulation.•Our results show that ignore the incubation period of the malaria parasite will overestimate the risk of malaria transmission. In this paper, a two-strain mathematical model is proposed to explore the effect of the incubation period of malaria parasites on the evolution of malaria. Firstly, ignoring the effect of incubation period in the mosquito, the basic reproduction number is calculated by the next generation matrix method. We proved that the disease is extinct and this model has a global asymptotical stabile disease-free equilibrium if the basic reproduction numbers of strains-1 and 2 are less than unity. Otherwise the disease is persistent and the strain-i dominant equilibrium is globally asymptotically stable if the reproduction number of stain-i is larger than unity and the reproduction number of stain-j is less than unity. Further, the similar results are obtained for the model with incubation period. In addition, we also consider the competitive exclusion phenomenon in two models. The sensitivity analysis shows that ignoring the incubation period of malaria will overestimate the risk of malaria transmission. Finally, some numerical simulations are performed to illustrate the main theoretical results.