scholarly journals A stage-structured SEIR model with time-dependent delays in an almost periodic environment

2020 ◽  
Vol 17 (6) ◽  
pp. 7732-7750
Author(s):  
Lizhong Qiang ◽  
◽  
Ren-Hu Wang ◽  
Ruofan An ◽  
Zhi-Cheng Wang ◽  
...  
Keyword(s):  
Time Dependent ◽  
Almost Periodic ◽  
Seir Model ◽  
Periodic Environment

scholarly journals Modelling of the second (and subsequent) waves of the coronavirus epidemic. Spain and Germany as case studies

2020 ◽  
Author(s):  
Francisco de Castro
Keyword(s):  
Case Studies ◽  
Mortality Rates ◽  
Time Dependent ◽  
Seir Model ◽  
Considerable Uncertainty ◽  
Second Wave

AbstractThe first wave of the coronavirus pandemic is waning in many countries. Some of them are starting to lift the confinement measures adopted to control it, but there is considerable uncertainty about if it is too soon and it may cause a second wave of the epidemic. To explore this issue, I fitted a SEIR model with time-dependent transmission and mortality rates to data from Spain and Germany as contrasting case studies. The model reached an excellent fit to the data. I then simulated the post-confinement epidemic under several scenarios. The model shows that (in the absence of a vaccine) a second wave is likely inevitable and will arrive soon, and that a strategy of adaptive confinement may be effective to control it. The model also shows that just a few days delay in starting the confinement may have caused and excess of thousands of deaths in Spain.

scholarly journals Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Wenhua Qiu ◽  
Jianguo Si
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Equilibrium Point ◽  
Almost Periodic Solution ◽  
Time Dependent ◽  
Almost Periodic ◽  
Degenerate Equilibrium ◽  
Periodic Transformation ◽  
Perturbed Equation ◽  
Kam Method

This paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic transformation. Hence, for the equation we can obtain a small almost-periodic solution.

scholarly journals Quantifying Effects, Forecasting Releases, and Herd Immunity of the Covid-19 Epidemic in S. Paulo – Brazil

2020 ◽  
Author(s):  
S. Celaschi
Keyword(s):  
Deterministic Model ◽  
Herd Immunity ◽  
Threshold Value ◽  
Basic Number ◽  
Time Dependent ◽  
Seir Model ◽  
Medical Facilities ◽  
Future Outcomes ◽  
The City ◽  
Mitigation Policies

AbstractA simple and well known epidemiological deterministic model was selected to estimate the main results for the basic dynamics of the Covid-19 epidemic breakout in the city of São Paulo – Brazil. The methodology employed the SEIR Model to characterize the epidemics outbreak and future outcomes. A time-dependent incidence weight on the SEIR reproductive basic number accounts for local Mitigation Policies (MP). The insights gained from analysis of these successful interventions were used to quantify shifts and reductions on active cases, casualties, and estimatives on required medical facilities (ITU). This knowledge can be applied to other Brazilian areas. The analysis was applied to forecast the consequences of releasing the MP over specific periods of time. Herd Immunity (HI) analysis allowed estimating how far we are from reaching the HI threshold value, and the price to be paid.

scholarly journals Modelling of the second (and subsequent) waves of the coronavirus epidemic. Spain and Germany as case studies

2020 ◽  
Author(s):  
Francisco de Castro
Keyword(s):  
Case Studies ◽  
Mortality Rates ◽  
Time Dependent ◽  
Seir Model ◽  
Considerable Uncertainty ◽  
Second Wave

Abstract The first wave of the coronavirus pandemic is waning in many countries. Some of them are starting to lift the confinement measures adopted to control it, but there is considerable uncertainty about if it is too soon and it may cause a second wave of the epidemic. To explore this issue, I fitted a SEIR model with time-dependent transmission and mortality rates to data from Spain and Germany as contrasting case studies. The model reached an excellent fit to the data. I then simulated the post-confinement epidemic under several scenarios. The model shows that (in the absence of a vaccine) a second wave is likely inevitable and will arrive soon, and that a strategy of adaptive confinement may be effective to control it. The model also shows that just a few days delay in starting the confinement may have caused and excess of thousands of deaths in Spain.

scholarly journals On annth-order infinitesimal generator and time-dependent operator differential equation with a strongly almost periodic solution

2002 ◽  
Vol 32 (9) ◽  
pp. 573-578 ◽  
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Infinitesimal Generator ◽  
Almost Periodic Solution ◽  
Time Dependent ◽  
Operator Differential Equation ◽  
Almost Periodic ◽  
Periodic Forcing ◽  
Forcing Function ◽  
Weakly Almost Periodic

In a Banach space, ifuis a Stepanov almost periodic solution of a certainnth-order infinitesimal generator and time-dependent operator differential equation with a Stepanov almost periodic forcing function, thenu,u′,…,u (n−2)are all strongly almost periodic andu (n−1)is weakly almost periodic.

scholarly journals MODELLING PRESYMPTOMATIC INFECTIOUSNESS IN COVID-19

2020 ◽  
Author(s):  
Russell Cheng ◽  
Christopher Dye ◽  
John Dagpunar ◽  
Brian Williams
Keyword(s):  
Control Strategies ◽  
Real Data ◽  
Compartment Model ◽  
Time Dependent ◽  
Seir Model ◽  
Continuous Simulation ◽  
Single Period ◽  
Infectious Stage

ABSTRACTThis paper considers SEPIR, the extension of an existing parametric SEIR continuous simulation compartment model. Both models can be fitted to real data as they include parameters that can simply be estimated from the data. However SEPIR deploys an additional presymptomatic (also called asymptomatic) infectious stage that is not included in SEIR but which is known to exist in COVID-19. This stage is also parametrised and so can be fitted to data. Both SEPIR and the existing SEIR model assume a homogeneous mixing population, an idealisation that is unrealistic in practice when dynamically varying control strategies are deployed against virus. This means that if either model is to represent more than just a single period in the behaviour of the epidemic, then the parameters of the model will have to be time dependent. This issue is also discussed in this paper.

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