Mathematical Analysis of the Ross–Macdonald Model with Quarantine

Abstract

People infected with malaria may receive less mosquito bites when they are treated in well-equipped hospitals or follow doctors’ advice for reducing exposure to mosquitoes at home. This quarantine-like intervention measure is especially feasible in countries and areas approaching malaria elimination. Motivated by mathematical models with quarantine for directly transmitted diseases, we develop a mosquito-borne disease model where imperfect quarantine is considered to mitigate the disease transmission from infected humans to susceptible mosquitoes. The basic reproduction number R is computed and the model equilibria and their stabilities are analyzed when the incidence rate is standard or bilinear. In particular, the model system may undergo a subcritical (backward) bifurcation at R= 1 when standard incidence is adopted, whereas the disease-free equilibrium is globally asymptotically stable as R≤ 1 and the unique endemic equilibrium is locally asymptotically stable as R> 1 when the infection incidence is bilinear. Numerical simulations suggest that the quarantine strategy can play an important role in decreasing malaria transmission. The success of quarantine mainly relies on the reduction of bites on quarantined individuals.