RESUMEN
A new network-based SIR epidemic model with saturated incidence rate and nonlinear recovery rate is proposed. We adopt an edge-compartmental approach to rewrite the system as a degree-edge-mixed model. The explicit formula of the basic reproduction number $ \mathit{\boldsymbol{R_{0}}} $ is obtained by renewal equation and Laplace transformation. We find that $ \mathit{\boldsymbol{R_{0}}} < 1 $ is not enough to ensure global asymptotic stability of the disease-free equilibrium, and when $ \mathit{\boldsymbol{R_{0}}} > 1 $, the system can exist multiple endemic equilibria. When the number of hospital beds is small enough, the system will undergo backward bifurcation at $ \mathit{\boldsymbol{R_{0}}} = 1 $. Moreover, it is proved that the stability of feasible endemic equilibrium is determined by signs of tangent slopes of the epidemic curve. Finally, the theoretical results are verified by numerical simulations. This study suggests that maintaining sufficient hospital beds is crucial for the control of infectious diseases.
RESUMEN
In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number R 0 is less than unity and unstable when R 0 > 1 . The analysis shows that the phenomenon of backward bifurcation occurs when R 0 < 1 . Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.
RESUMEN
OBJECTIVES: We study the transmission dynamics of cholera in the presence of limited resources, a common feature of the developing world. The model is used to gain insight into the impact of available resources of the health care system on the spread and control of the disease. A deterministic model that includes a nonlinear recovery rate is formulated and rigorously analyzed. Limited treatment is described by inclusion of a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings. RESULTS: The model analysis shows that the disease free steady state is locally stable when the threshold [Formula: see text]. It is also shown that the model has multiple equilibria and the model exhibits the phenomenon of backward bifurcation whose implications to cholera infection are discussed. The results are useful for the public health planning in resource allocation for the control of cholera transmission.
Asunto(s)
Cólera/prevención & control , Capacidad de Camas en Hospitales/estadística & datos numéricos , Hospitales/estadística & datos numéricos , Modelos Estadísticos , Salud Pública/estadística & datos numéricos , Cólera/economía , Cólera/epidemiología , Cólera/transmisión , Simulación por Computador , Países en Desarrollo , Humanos , Salud Pública/economía , Salud Pública/métodos , Vibrio cholerae/patogenicidad , Zimbabwe/epidemiologíaRESUMEN
A deterministic model for the transmission dynamics of dengue fever is formulated to study, with a nonlinear recovery rate, the impact of available resources of the health system on the spread and control of the disease. Model results indicate the existence of multiple endemic equilibria, as well as coexistence of an endemic equilibrium with a periodic solution. Additionally, our model exhibits the phenomenon of backward bifurcation. The results of this study could be helpful for public health authorities in their planning of a proper resource allocation for the control of dengue transmission.