A Stochastic SEIRS Epidemic Model with Infection Forces and Intervention Strategies

The spread of epidemics has been extensively investigated using susceptible-exposed infectious-recovered-susceptible (SEIRS) models. In this work, we propose a SEIRS pandemic model with infection forces and intervention strategies. The proposed model is characterized by a stochastic differential equation (SDE) framework with arbitrary parameter settings. Based on a Markov semigroup hypothesis, we demonstrate the effect of the proliferation number R 0 S on the SDE solution. On the one hand, when R 0 S < 1 , the SDE has an illness-free solution set under gentle additional conditions. This implies that the epidemic can be eliminated with a likelihood of 1. On the other hand, when R 0 S > 1 , the SDE has an endemic stationary circulation under mild additional conditions. This prompts the stochastic regeneration of the epidemic. Also, we show that arbitrary fluctuations can reduce the infection outbreak. Hence, valuable procedures can be created to manage and control epidemics.

Dynamical Analysis of an SEIRS Model With Incomplete Recovery and Relapse on Networks and Its Optimal Vaccination Control

For some infectious diseases, such as herpes and tuberculosis, there is incomplete recovery and relapse. These phenomena make them difficult to control. In consequence of this status, an SEIRS epidemic model with incomplete recovery and relapse on networks is established and the global dynamics is studied. The results show that when the basic reproduction number R 0 <=1 the disease-free equilibrium is globally asymptotically stable; when R 0 > 1, the endemic equilibrium is globally asymptotically stable. In addition, in consideration of vaccination control strategy, an SVEIRS model is introduced and the optimal control is solved. At last, the theoretical results are illustrated with numerical simulations.

An SEIRS Epidemic Model with Immigration and Vertical Transmission

The study indicates that we should improve the model by introducing the immigration rate in the model to control the spread of disease. An SEIRS epidemic model with Immigration and Vertical Transmission and analyzed the steady state and stability of the equilibrium points. The model equations were solved analytically. The stability of the both equilibrium are proved by Routh-Hurwitz criteria. We see that if the basic reproductive number R0<1 then the disease free equilibrium is locally asymptotically stable and if R0<1 the endemic equilibrium will be locally asymptotically stable.