Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China.
College of Mathematical Sciences, Harbin Engineering University, 150001, Harbin, China.
Bull Math Biol. 2020 Apr 2;82(4):47. doi: 10.1007/s11538-020-00723-0.
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 [Formula: see text] 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 [Formula: see text] when standard incidence is adopted, whereas the disease-free equilibrium is globally asymptotically stable as [Formula: see text] and the unique endemic equilibrium is locally asymptotically stable as [Formula: see text] 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.
当疟疾病人在设备齐全的医院接受治疗或遵循医生的建议减少在家中接触蚊子时，他们可能会受到较少的蚊子叮咬。这种类似隔离的干预措施在接近消除疟疾的国家和地区特别可行。受具有隔离的直接传播疾病的数学模型启发，我们开发了一种蚊媒疾病模型，其中考虑到不完善的隔离措施，以减轻感染人类向易感蚊子传播疾病的风险。当发病率为标准或双线性时，计算基本繁殖数[Formula: see text]，并分析模型平衡点及其稳定性。特别是，当采用标准发病率时，模型系统可能会在[Formula: see text]处发生亚临界（回溯）分岔，而当感染发病率为双线性时，无病平衡点在[Formula: see text]处全局渐近稳定，唯一的地方平衡点在[Formula: see text]处局部渐近稳定。数值模拟表明，隔离策略可以在减少疟疾传播方面发挥重要作用。隔离的成功主要取决于减少对隔离个体的叮咬。
