We investigate the stability of an SIR epidemic model with stage structure and time delay. By analyzing the eigenvalues of the corresponding characteristic equation, the local stability of each feasible equilibrium of the model is established. By using comparison arguments, it is proved when the basic reproduction number is less than unity, the disease free equilibrium is globally asymptoticall...

*Correspondence: [email protected]; [email protected] 1Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan 2Faculty of Information Technology, University of Central Punjab, Lahore, Pakistan Full list of author information is available at the end of the article Abstract A non-linear mathematical model with non-integer order γ , 0 < γ ≤ 1, is used to a...

An SEIR model with vaccination strategy that incorporates distinct incidence rates for the exposed and the infected populations is studied. By means of Lyapunov function and LaSalle's invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. The sufficient conditions for the global stability of the endemic equilibrium are obtained using the compoun...

In this paper, a model is proposed to study the impact of awareness on the dynamics of dengue. It is assumed that due to awareness of the disease some susceptible take necessary precautionary measures to protect themselves from mosquito bite. A threshold is obtained for the stability of the disease-free equilibrium state. The awareness is found to affect the threshold. For the sufficiently larg...

A delayed mathematical model of Dengue dynamical transmission between vector mosquitoes and human, incorporating a control strategy of perfect pediatric vaccination is proposed in this paper. By some analytical skills, we obtain the existence of disease-free equilibria and endemic equilibrium, the necessary conditions of global asymptotical stability about two disease-free equilibria. Further, ...

The paper considers continuous-time networked susceptible-infected-susceptible (SIS) diseases spreading over a population. Each agent represents sub-population and has its own healing rate infection rate; the state of at time instant denotes what fraction said is infected with disease instant. By taking account changes in behaviors agents response to rates real-time, our goal devise feedback st...

Infectious diseases continue to be a significant threat human health and civilization, finding effective methods combat them is crucial. In this paper, we investigate the impact of awareness campaigns optimal control techniques on infectious without proper vaccines. Specifically, develop an SIRS-type mathematical model that incorporates through media treatment for disease transmission dynamics ...

In this paper, we have proposed and analyzed a nonlinear mathematical model for the spread of Polio in a population with variable size structure including the role of vaccination. A threshold parameter, R , is found that completely determines the stability dynamics and outcome of the disease. It is found that if 1  R , the disease free equilibrium is stable and the disease dies out. However, i...

This paper demonstrates input-to-state stability (ISS) of the SIR model infectious diseases with respect to disease-free equilibrium and endemic equilibrium. Lyapunov functions are constructed verify that both equilibria individually robust perturbation newborn/immigration rate which determines eventual state populations in epidemics. The construction analysis geome...