scholarly journals Modeling of the COVID-19 pandemic in the limit of no acquired immunity

2021 ◽  
Vol 8 (2) ◽  
pp. 282-303
Author(s):  
J. M. Ilnytskyi ◽  
Keyword(s):  
Analytic Solution ◽  
Effective Vaccine ◽  
Acquired Immunity ◽  
Approximate Analytic Solution ◽  
Contact Rate ◽  
Reproduction Ratio ◽  
Numeric Solution ◽  
The One ◽  
Disease Free ◽  
Rate Threshold

We propose the SEIRS compartmental epidemiology model aimed at modeling the COVID-19 pandemy dynamics. The limit case of no acquired immunity (neither natural nor via vaccination) is considered mimicking the situation (i) when no effective vaccine being developed or available yet, and (ii) the virus strongly mutates causing massive reinfections. Therefore, the only means of suppressing the virus spread are via quarantine measures and effective identification and isolation of infected individuals. We found both the disease-free and the endemic fixed points and examined their stability. The basic reproduction ratio is obtained and its dependence on the parameters of the model is discussed. We found the presence of the contact rate threshold beyond which the disease-free fixed point cannot be reached. Using the numeric solution, the approximate analytic solution of the model, characterized by rescaled contact rate, is obtained. Several possible "quarantine on"/"quarantine off" scenarios are considered and the one combined with flexible adjustment of the identification and isolation rates is found to be the most effective in bringing the second and consequent waves down. The study can be interpreted as a reference point for the case when the natural or acquired immunity, as well as vaccination, are taken into account. It will be a topic of a separate study.

Simple Approximate Solutions for Dynamic Response of Suspension System

2022 ◽  
Vol 21 ◽  
pp. 20-31
Author(s):  
Jacob Nagler
Keyword(s):  
Analytic Solution ◽  
Approximate Solutions ◽  
Quantitative Agreement ◽  
Gravitational Energy ◽  
Suspension System ◽  
Approximate Analytic Solution ◽  
Stiffness Properties ◽  
Coupling Case ◽  
The One ◽  
The Impact

An approximate simplified analytic solution is proposed for the one DOF (degree of freedom) static and dynamic displacements alongside the stiffness (dynamic and static) and damping coefficients (minimum and maximum/critical values) of a parallel spring-damper suspension system connected to a solid mass-body gaining its energy by falling from height h. The analytic solution for the prescribed system is based on energy conservation equilibrium, considering the impact by a special G parameter. The formulation is based on the works performed by Timoshenko (1928), Mindlin (1945), and the U. S. army-engineering handbook (1975, 1982). A comparison between the prescribed studies formulations and current development has led to qualitative agreement. Moreover, quantitative agreement was found between the current prescribed suspension properties approximate value - results and the traditionally time dependent (transient, frequency) parameter properties. Also, coupling models that concerns the linkage between different work and energy terms, e.g., the damping energy, friction work, spring potential energy and gravitational energy model was performed. Moreover, approximate analytic solution was proposed for both cases (friction and coupling case), whereas the uncoupling and the coupling cases were found to agree qualitatively with the literature studies. Both coupling and uncoupling solutions were found to complete each other, explaining different literature attitudes and assumptions. In addition, some design points were clarified about the wire mounting isolators stiffness properties dependent on their physical behavior (compression, shear tension), based on Cavoflex catalog. Finally, the current study aims to continue and contribute the suspension, package cushioning and containers studies by using an initial simple pre – design analytic evaluation of falling mass- body (like cushion, containers, etc.).

scholarly journals COVID-19: Risks of Re-emergence, Re-infection, and Control Measures -- A Long Term Modelling Study

2020 ◽  
Author(s):  
Subhas Kumar Ghosh ◽  
Sachchit Ghosh
Keyword(s):  
Control Measures ◽  
Effective Vaccine ◽  
Acquired Immunity ◽  
Model Parameters ◽  
Contact Rate ◽  
Spread Of Infection ◽  
And Control ◽  
Current Stage ◽  
Potential Peak

In this work we define a modified SEIR model that accounts for the spread of infection during the latent period, infections from asymptomatic or pauci-symptomatic infected individuals, potential loss of acquired immunity, people's increasing awareness of social distancing and the use of vaccination as well as non-pharmaceutical interventions like social confinement. We estimate model parameters in three different scenarios - in Italy, where there is a growing number of cases and re-emergence of the epidemic, in India, where there are significant number of cases post confinement period and in Victoria, Australia where a re-emergence has been controlled with severe social confinement program. Our result shows the benefit of long-term confinement of 50% or above population and extensive testing. With respect to loss of acquired immunity, our model suggests higher impact for Italy. We also show that a reasonably effective vaccine with mass vaccination program can be successful in significantly controlling the size of infected population. We show that for India, a reduction in contact rate by 50% compared to a reduction of 10% in the current stage can reduce death from 0.0268% to 0.0141% of population. Similarly, for Italy we show that reducing contact rate by half can reduce a potential peak infection of 15% population to less than 1.5% of population, and potential deaths from 0.48% to 0.04%. With respect to vaccination, we show that even a 75% efficient vaccine administered to 50% population can reduce the peak number of infected populations by nearly 50% in Italy. Similarly, for India, a 0.056% of population would die without vaccination, while 93.75% efficient vaccine given to 30% population would bring this down to 0.036% of population, and 93.75% efficient vaccine given to 70% population would bring this down to 0.034%.

scholarly journals Stability analysis of a dynamical model of tuberculosis with incomplete treatment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ihsan Ullah ◽  
Saeed Ahmad ◽  
Qasem Al-Mdallal ◽  
Zareen A. Khan ◽  
Hasib Khan ◽  
...  
Keyword(s):  
Disease Transmission ◽  
Contact Rate ◽  
Asymptotically Stable ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Efficient Treatment ◽  
Effective Contact ◽  
The Impact ◽  
Incomplete Treatment

Abstract A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. We also analyze the asymptotic behavior, spread, and possible eradication of the TB infection. It is observed that the disease transmission dynamics is characterized by the basic reproduction ratio $\Re _{0}$ ℜ 0 ; if $\Re _{0}<1$ ℜ 0 < 1 , there is only a disease-free equilibrium which is both locally and globally asymptotically stable. Moreover, for $\Re _{0}>1$ ℜ 0 > 1 , a unique positive endemic equilibrium exists which is globally asymptotically stable. The global stability of the equilibria is shown via Lyapunov function. It is also obtained that incomplete treatment of TB causes increase in disease infection while efficient treatment results in a reduction in TB. Finally, for the estimated parameters, some numerical simulations are performed to verify the analytical results. These numerical results indicate that decrease in the effective contact rate λ and increase in the treatment rate γ play a significant role in the TB infection control.

scholarly journals AN ANALYTIC SOLUTION FOR ONE-DIMENSIONAL DISSIPATIONAL STRAIN-GRADIENT PLASTICITY

2009 ◽  
Vol 50 (3) ◽  
pp. 407-420
Author(s):  
ROGER YOUNG
Keyword(s):  
Boundary Condition ◽  
Strain Gradient ◽  
Analytic Solution ◽  
Strain Gradient Plasticity ◽  
Numerical Results ◽  
Gradient Plasticity ◽  
One Dimensional ◽  
Numerical Result ◽  
Formulation Analysis ◽  
The One

AbstractAn analytic solution is developed for the one-dimensional dissipational slip gradient equation first described by Gurtin [“On the plasticity of single crystals: free energy, microforces, plastic strain-gradients”, J. Mech. Phys. Solids48 (2000) 989–1036] and then investigated numerically by Anand et al. [“A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results”, J. Mech. Phys. Solids53 (2005) 1798–1826]. However we find that the analytic solution is incompatible with the zero-sliprate boundary condition (“clamped boundary condition”) postulated by these authors, and is in fact excluded by the theory. As a consequence the analytic solution agrees with the numerical results except near the boundary. The equation also admits a series of higher mode solutions where the numerical result corresponds to (a particular case of) the fundamental mode. Anand et al. also established that the one-dimensional dissipational gradients strengthen the material, but this proposition only holds if zero-sliprate boundary conditions can be imposed, which we have shown cannot be done. Hence the possibility remains open that dissipational gradient weakening may also occur.

scholarly journals The Global Behavior of a Periodic Epidemic Model with Travel between Patches

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Luosheng Wen ◽  
Bin Long ◽  
Xin Liang ◽  
Fengling Zeng
Keyword(s):  
Epidemic Model ◽  
Transmission Rate ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Periodic Transmission ◽  
Theoretical Results ◽  
Disease Free

We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratioR0and two theorems on the global behavior: ifR0< 1 the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then it is unstable; ifR0> 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.

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