scholarly journals Protection after Quarantine: Insights from a Q-SEIR Model with Nonlinear Incidence Rates Applied to COVID-19

2020 ◽  
Author(s):  
Jose Marie Antonio Minoza ◽  
Jesus Emmanuel Sevilleja ◽  
Romulo de Castro ◽  
Salvador E. Caoili ◽  
Vena Pearl Bongolan
Keyword(s):  
Reproduction Number ◽  
Incidence Rates ◽  
Health Promoting Behaviors ◽  
Strict Adherence ◽  
Seir Model ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates ◽  
Health Promoting ◽  
Two Parameters ◽  
Disease Free

AbstractCommunity quarantine has been resorted to by various governments to address the current COVID-19 pandemic; however, this is not the only non-therapeutic method of effectively controlling the spread of the infection. We study an SEIR model with nonlinear incidence rates, and introduce two parameters, α and ε, which mimics the effect of quarantine (Q). We compare this with the Q-SEIR model, recently developed, and demonstrate the control of COVID-19 without the stringent conditions of community quarantine. We analyzed the sensitivity and elasticity indices of the parameters with respect to the reproduction number. Results suggest that a control strategy that involves maximizing α and ε is likely to be successful, although quarantine is still more effective in limiting the spread of the virus. Release from quarantine depends on continuance and strict adherence to recommended social and health promoting behaviors. Furthermore, maximizing α and ε is equivalent to a 50% successful quarantine in disease-free equilibrium (DFE). This model reduced the infectious in Quezon City by 3.45% and Iloilo Province by 3.88%; however, earlier peaking by nine and 17 days, respectively, when compared with the results of Q-SEIR.

scholarly journals Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Feng Wang ◽  
Shan Wang ◽  
Youhua Peng
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Perturbation ◽  
Incidence Rates ◽  
Nonlinear Incidence Rate ◽  
Stochastic Perturbations ◽  
Seir Model ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates ◽  
Uniqueness Of The Solution ◽  
Rate Functions

In this paper, the asymptotic behavior of a multigroup SEIR model with stochastic perturbations and nonlinear incidence rate functions is studied. First, the existence and uniqueness of the solution to the model we discuss are given. Then, the global asymptotical stability in probability of the model with R0<1 is established by constructing Lyapunov functions. Next, we prove that the disease can die out exponentially under certain stochastic perturbation while it is persistent in the deterministic case when R0>1. Finally, several examples and numerical simulations are provided to illustrate the dynamic behavior of the model and verify our analytical results.

scholarly journals Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Ozair
Keyword(s):  
Global Analysis ◽  
Horizontal Transmission ◽  
Disease Model ◽  
Pine Wilt Disease ◽  
Incidence Rates ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Pine Wilt ◽  
Nonlinear Incidence Rates

The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free” equilibrium always exists and is globally asymptotically stable wheneverR0≤1. Furthermore, the disease persists at an “endemic” level when the reproductive number exceeds unity.

Dynamics of a delayed epidemic model with varying immunity period and nonlinear transmission

2015 ◽  
Vol 08 (02) ◽  
pp. 1550027 ◽  
Author(s):  
Aadil Lahrouz
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Incidence Rates ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
The Basic Reproduction Number

An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the community when the number of infectives is getting larger. The distributed delay is derived to describe the dynamics of infectious diseases with varying immunity. Lyapunov functionals are used to show that the disease-free equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one. Moreover, it is shown that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions under which the endemic equilibrium is locally and globally asymptotically stable are obtained.

scholarly journals Dynamic Analysis of an SEIR Model with Distinct Incidence for Exposed and Infectives

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Junhong Li ◽  
Ning Cui
Keyword(s):  
Matrix Theory ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Vaccination Strategy ◽  
Invariant Set ◽  
Incidence Rates ◽  
Seir Model ◽  
Asymptotical Stable ◽  
Compound Matrix ◽  
Disease Free

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 compound matrix theory. Furthermore, the method of direct numerical simulation of the system shows that there is a periodic solution, when the system has three equilibrium points.

scholarly journals Dynamics of a Diffusive Multigroup SVIR Model with Nonlinear Incidence

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Jinhu Xu ◽  
Yan Geng
Keyword(s):  
Reproduction Number ◽  
Classical Method ◽  
Reaction Diffusion ◽  
Theoretic Approach ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Special Case ◽  
Disease Free

In this paper, a multigroup SVIR epidemic model with reaction-diffusion and nonlinear incidence is investigated. We first establish the well-posedness of the model. Then, the basic reproduction number ℜ 0 is established and shown as a threshold: the disease-free steady state is globally asymptotically stable if ℜ 0 < 1 , while the disease will be persistent when ℜ 0 > 1 . Moreover, applying the classical method of Lyapunov and a recently developed graph-theoretic approach, we established the global stability of the endemic equilibria for a special case.

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