The unprecedented scale and rapidity of dissemination of re-emerging and emerging infectious diseases impose new challenges for regulators and health authorities. To curb the dispersal of such diseases, proper management of healthcare facilities and vaccines are core drivers. In the present work, we assess the unified impact of healthcare facilities and vaccination on the control of an infectious disease by formulating a mathematical model. To formulate the model for any region, we consider four classes of human population; namely, susceptible, infected, hospitalized, and vaccinated. It is assumed that the increment in number of beds in hospitals is continuously made in proportion to the number of infected individuals. To ensure the occurrence of transcritical, saddle–node and Hopf bifurcations, the conditions are derived. The normal form is obtained to show the existence of Bogdanov–Takens bifurcation. To validate the analytically obtained results, we have conducted some numerical simulations. These results will be useful to public health authorities for planning appropriate health care resources and vaccination programs to diminish prevalence of infectious diseases.

重新出现和新出现的传染病的传播规模和速度前所未有，给监管机构和卫生当局带来了新的挑战。为了遏制此类疾病的传播，医疗设施和疫苗的适当管理是核心驱动力。在目前的工作中，我们通过制定数学模型来评估医疗设施和疫苗接种对传染病控制的统一影响。为了制定任何地区的模型，我们考虑四类人口；即易感者、感染者、住院者和接种疫苗者。假设医院床位数量按照感染人数的比例不断增加。为了确保跨临界、鞍结和 Hopf 分岔的发生，导出了条件。得到的范式表明了 Bogdanov-Takens 分岔的存在。为了验证分析获得的结果，我们进行了一些数值模拟。这些结果将有助于公共卫生当局规划适当的医疗保健资源和疫苗接种计划，以减少传染病的流行。