Mathematical Analysis Of The Ross-Macdonald Model With Quarantine

Malaria is an infectious disease caused by the Plasmodium parasite that is transmitted among humans through the bites of female Anopheles mosquitoes,which is currently the most harmful mosquito-borne disease and seriously threatens nearly half of the world's population.In reality,malaria-infected people who receive healthcare and treatment at home or in hospital usually get less mosquito bites.Based on the classical Ross-Macdonald mosquito-borne disease model,we introduce a compartment for quarantined people and propose a malaria model with imperfect quarantine.By using the theory and method in differential equations and infectious disease modeling,we define the basic reproduction number?₀of the model and study the existence and stability of equilibria.In particular,the system may undergo backward bifurcation at?₀=1 when standard incidence is adopted,while the disease-free equilibrium is globally asymptotically stable as?₀<1when the incidence is bilinear.Numerical simulations suggest that the quarantine measure plays an important role in reducing malaria transmission.