Estimating the impact of interventions against COVID-19: From lockdown to vaccination

Coronavirus disease 2019 (COVID-19) is an infectious disease of humans caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since the first case was identified in China in December 2019 the disease has spread worldwide, leading to an ongoing pandemic. In this article, we present an agent-based model of COVID-19 in Luxembourg, and use it to estimate the impact, on cases and deaths, of interventions including testing, contact tracing, lockdown, curfew and vaccination. Our model is based on collation, with agents performing activities and moving between locations accordingly. The model is highly heterogeneous, featuring spatial clustering, over 2000 behavioural types and a 10 minute time resolution. The model is validated against COVID-19 clinical monitoring data collected in Luxembourg in 2020. Our model predicts far fewer cases and deaths than the equivalent equation-based SEIR model. In particular, with R0 = 2.45, the SEIR model infects 87% of the resident population while our agent-based model infects only around 23% of the resident population. Our simulations suggest that testing and contract tracing reduce cases substantially, but are less effective at reducing deaths. Lockdowns are very effective although costly, while the impact of an 11pm-6am curfew is relatively small. When vaccinating against a future outbreak, our results suggest that herd immunity can be achieved at relatively low coverage, with substantial levels of protection achieved with only 30% of the population fully immune. When vaccinating in the midst of an outbreak, the challenge is more difficult. In this context, we investigate the impact of vaccine efficacy, capacity, hesitancy and strategy. We conclude that, short of a permanent lockdown, vaccination is by far the most effective way to suppress and ultimately control the spread of COVID-19.

A new derivation of the relationship between diffusion coefficient and entropy in classical Brownian motion by the ensemble method

The diffusion coefficient–a measure of dissipation, and the entropy–a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the correlation is often strongly non-linear. To understand this complex dependence, we consider the classical Brownian diffusion in this work. Under certain rational assumption, i.e. in the bi-component fluid mixture, the mass of the Brownian particle MM is far greater than that of the bath molecule mm, we can adopt the weakly couple limit. Only considering the first-order approximation of the mass ratio m/Mm/M, we obtain a linear motion equation in the reference frame of the observer as a Brownian particle. Based on this equivalent equation, we get the Hamiltonian at equilibrium. Finally, using canonical ensemble method, we define a new entropy that is similar to the Kolmogorov-Sinai entropy. Further, we present an analytic expression of the relationship between the diffusion coefficient DD and the entropy SS in the thermal equilibrium, that is to say, D =\frac{\hbar}{eM} \exp{[S/(k_Bd)]}D=ℏeMexp[S/(kBd)], where dd is the dimension of the space, k_BkB the Boltzmann constant, h the reduced Planck constant and ee the Euler number. This kind of scaling relation has been well-known and well-tested since the similar one for single component is firstly derived by Rosenfeld with the expansion of volume ratio.

Curved Space: Theory of Everything

Matter and energy are both made from curved space, the flow of space creates gravitation, and the increase of space causes the expansion of the universe. Matter curves in two different directions of one dimension creates two types of electric charges: positive and negative. Matter curves in three different dimensions creates three values or charges of quark's color: red, green, and blue. The equivalent equation of space: S=Ec²=mc⁴ . The gravitation of hollow sphere space: Sμν=4πGm=(4/3)π((r+a)³-r³) .

Solitary wave solutions in two-Core optical fibers with coupling-coefficient dispersion and Kerr nonlinearity

In this paper, we studies chirped solitary waves in two-Core optical fibers with coupling-coefficient dispersion and intermodal dispersion. To construct chirp soliton, the couple of nonlinear Schrödinger equation which describing the pulses propagation along the two-core fiber have been reduced to one equivalent equation. By adopting the traveling-waves hypothesis, the exact analytical solutions of the GNSE were obtained by using three relevant mathematical methods namely the auxiliary equation method, the modified auxiliary equation method and the Sine-Gordon expansion approach. Lastly, the behavior of the chirped like-soliton solutions were discussed and some contours of the plot evolution of the bright and dark solitons are obtained.

Curved Space: Theory of Everything

Matter and energy are both made from curved space, the flow of space creates gravitation, and the increase of space causes the expansion of the universe. Matter curves in two different directions of one dimension creates two types of electric charges: positive and negative. Matter curves in three different dimensions creates three values or charges of quark's color: red, green, and blue. The equivalent equation of space: S=Ec²=mc⁴ . The main asteroid belt is at the gravitation limit distance of the Sun. When the Sun moves forward in the Milky Way, the inner planets are affected by the gravitation and moves directly with it. The space which released by the Sun flows backwards on its path and guiding the outer planets to follow it. The gravitation of hollow sphere space: S=(4/3)π((r+a)³-r³) .

Estimating the impact of interventions against COVID-19: from lockdown to vaccination

Coronavirus disease 2019 (COVID-19) is an infectious disease of humans caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since the first case was identified in China in December 2019 the disease has spread worldwide, leading to an ongoing pandemic. In this article, we present a detailed agent-based model of COVID-19 in Luxembourg, and use it to estimate the impact, on cases and deaths, of interventions including testing, contact tracing, lockdown, curfew and vaccination.Our model is based on collation, with agents performing activities and moving between locations accordingly. The model is highly heterogeneous, featuring spatial clustering, over 2000 behavioural types and a 10 minute time resolution. The model is validated against COVID-19 clinical monitoring data collected in Luxembourg in 2020.Our model predicts far fewer cases and deaths than the equivalent equation-based SEIR model. In particular, with R0 = 2.45, the SEIR model infects 87% of the resident population while our agent-based model results, on average, in only around 23% of the resident population infected. Our simulations suggest that testing and contract tracing reduce cases substantially, but are much less effective at reducing deaths. Lockdowns appear very effective although costly, while the impact of an 11pm-6am curfew is relatively small. When vaccinating against a future outbreak, our results suggest that herd immunity can be achieved at relatively low levels, with substantial levels of protection achieved with only 30% of the population immune. When vaccinating in midst of an outbreak, the challenge is more difficult. In this context, we investigate the impact of vaccine efficacy, capacity, hesitancy and strategy.We conclude that, short of a permanent lockdown, vaccination is by far the most effective way to suppress and ultimately control the spread of COVID-19.

Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay

In this paper, we prove the existence and uniqueness of a mild solution to the system of ψ- Hilfer neutral fractional evolution equations with infinite delay H 𝔻0 αβ;ψ [x(t) − h(t, xt )] = A x(t) + f (t, x(t), xt ), t ∈ [0, b], b > 0 and x(t) = ϕ(t), t ∈ (−∞, 0]. We first obtain the Volterra integral equivalent equation and propose the mild solution of the system. Then, we prove the existence and uniqueness of solution by using the Banach contraction mapping principle and the Leray-Schauder alternative theorem.

The Split Feasibility Problem with Some Projection Methods in Banach Spaces

In this paper, we study the split feasibility problem in Banach spaces. At first, we prove that a solution of this problem is a solution of the equivalent equation defined by using a metric projection, a generalized projection, and sunny generalized nonexpansive retraction, respectively. Then, using the hybrid method with these projections, we prove strong convergence theorems in mathematical programing in order to find a solution of the split feasibility problem in Banach spaces.

Curved Space: Theory of Everything

Matter and energy are made from curved space, the flow of space creates gravity, and the increase of the space causes the expansion of the universe. Space curves in two different directions of another dimension create two types of electric charge: positive and negative. Space curves in three different dimensions creates three values or charges of quark's color: red, green, and blue. The equivalent equation of space: S=Ec²=mc⁴.

Crystal structure, thermal properties and detonation characterization of bis(5-amino-1,2,4-triazol-4-ium-3-yl)methane dinitrate

Bis(5-amino-1,2,4-triazol-4-ium-3-yl)methane dinitrate, BATZM·(NO3)2 or C5H10N8 2+·2NO3 −, was synthesized and its crystal structure determined by single-crystal X-ray diffraction. It crystallizes in the space group Pbcn (orthorhombic) with Z = 4. BATZM·(NO3)2 is a V-shaped molecule where hydrogen bonds form a two-dimensional corrugated sheet with reasonable chemical geometry and no disorder. The specific molar heat capacity (C p,m) of BATZM·(NO3)2 was determined using the continuous C p mode of a microcalorimeter and theoretical calculations, and the C p,m value is 366.14 J K−1 mol−1 at 298.15 K. The relative deviations between the theoretical and experimental values of C p,m, HT – H 298.15K and ST – S 298.15K of BATZM·(NO3)2 are almost equivalent at each temperature. The detonation velocity (D) and detonation pressure (P) were estimated using the nitrogen equivalent equation according to the experimental density; BATZM·(NO3)2 has a higher detonation velocity (7927.47 ± 3.63 m s−1) and detonation pressure (27.50 ± 0.03 GPa) than 2,4,6-trinitrotoluene (TNT). The above results for BATZM·(NO3)2 are compared with those of bis(5-amino-1,2,4-triazol-3-yl)methane (BATZM) and bis(5-amino-1,2,4-triazol-4-ium-3-yl)methane dihydrochloride (BATZM·Cl2), and the effect of nitrate formation is discussed.