Future worldwide coronavirus disease 2019 epidemic predictions by Gaidai multivariate risk evaluation method

Abstract Accurate estimation of pandemic likelihood in every US state of interest and at any time. Coronavirus disease 2019 (COVID‐19) is an infectious illness with a high potential for global dissemination and low rates of fatality and morbidity, placing some strains on national public health systems. This research intends to benchmark a novel technique, that enables hazard assessment, based on available clinical data, and dynamically observed patient numbers while taking into account pertinent territorial and temporal mapping. Multicentre, population‐based, and biostatistical strategies have been utilized to process raw/unfiltered medical survey data. The expansion of extreme value statistics from the univariate to the bivariate situation meets with numerous challenges. First, the univariate extreme value types theorem cannot be directly extended to the bivariate (2D) case,—not to mention challenges with system dimensionality higher than 2D. Assessing outbreak risks of future outbreaks in any nation/region of interest. Existing bio‐statistical approaches do not always have the benefits of effectively handling large regional dimensionality and cross‐correlation between various regional observations. These methods deal with temporal observations of multi‐regional phenomena. Apply contemporary, novel statistical/reliability techniques directly to raw/unfiltered clinical data. The current study outlines a novel bio‐system hazard assessment technique that is particularly suited for multi‐regional environmental, bio, and public health systems, observed over a representative period. With the use of the Gaidai multivariate hazard assessment approach, epidemic outbreak spatiotemporal risks may be properly assessed. Based on raw/unfiltered clinical survey data, the Gaidai multivariate hazard assessment approach may be applied to a variety of public health applications. The study's primary finding was an assessment of the risks of epidemic outbreaks, along with a matching confidence range. Future global COVID‐19/severe acute respiratory syndrome coronavirus 2 (SARS‐COV2) epidemic risks have been examined in the current study; however, COVID‐19/SARS‐COV2 infection transmission mechanisms have not been discussed.

0][21][22][23][24][25][26] Further studies on statistical variances per nation have been provided. 27[29][30][31][32][33][34][35] Authors utilized EVT (i.e., Extreme Value Theory), to assess the risks of a worldwide influenza pandemic, suggesting prospective projections for epidemic risks. 9Similarly, 10 utilized EVT to predict and identify flu epidemic abnormalities.Due to a lack of statistical research to forecast multivariate risks of influenza and infectious disease outbreaks, the authors suggested a novel multivariate approach, providing improved insight and predictors.Given that epidemic outbreaks are viewed as unanticipated events, that might occur at any time and in any region/country, the current study employs a spatiotemporal approach.To forecast pandemic risks, wherever they may occur, specific non-dimensional factors have been introduced.February 2020 to the end of 2022 had been retrieved from a public source. 1The global biological system under investigation may be modeled as an MDOF (i.e., multi-degree of freedom) bio-dynamic system, with strongly inter-correlated regional/national key/critical components/dimensions.Several recent researchers have previously utilized advanced statistical techniques, to forecast COVID-19/SARS-COV2 progression; for linear log models. 21though the main goal of this study was to predict future epidemic outbreak risks, this study solely concentrated on daily numbers of newly reported cases, ignoring symptoms themselves.For detailed information related to so-called long-lasting COVID-19/SARS-COV2 symptoms, or the "long COVID".For more details on mortality study see. 12,14A global map with COVID-19/SARS-COV2 cases is given in Figure 2.

GAIDAI MULTIVARIATE RISKS EVALUATION METHOD
The underlying epidemiological process has been considered in this analysis to be seasonally variable, but statistically representative across 2 (2020-2022) years of continuous clinical observation.This study was based on the quasi-stationarity assumption.The problem of the underlying tendency/trend has to be addressed given a longer time horizon, for example, 10-100 years. 8[46][47][48] Considering piecewise jointly-stationary, MDOF environmental public health dynamic biosystem, having its key/critical components X(t), Y(t), Z(t), … being part of biosystem's dynamic MDOF time-record (X(t), Y(t), Z(t), …), observed/recorded/measured over sufficient (i.e., representative) timelapse (0, T).
etc., being quite similar.It had been assumed that all environmental public health biosystems' critical components' local maxima are nonnegative.The goal was to accurately determine risks of dynamic environmental public health biosystem's hazard/failure risk/probability related to the target biosystem's survival chances/ probability P, being expressed as T , … being target joint PDF of principal component's global maxima, over observational timelapse (0, T).Next, MDOF public health system's vector (X(t), Y(t), Z(t), …) to be scaled to the nondimensional . . .It is not practicable to straightforwardly assess the latter public health system's joint PDF, due to the public health biosystem's multi-dimensionality, along with given limitations of the underlying raw clinical dataset.
More specifically, the environmental dynamic system is considered to have failed/damaged, or entered into a state of hazard, when either biosystem's critical components X(t) exceeds  X ; or Y(t) exceeds  Y ; or Z(t) exceeds  Z , etc.,-or, equivalently, when either X, Ỹ, Z, … exceeds 1.
Let one arrange the public health system's key component's local max- ] into a single temporal merged bio-systems vector, t 1 ≤ ⋯ ≤ t N , in a monotonously non-decreasing temporal order, having  now being as follows: To account for dependencies between neighboring R j , a 1-step public health biosystem's memory approximation (conditioning memory for 2 ≤ j ≤ N with conditioning memory depth number k = 2. Equation (3) may be now expressed as with 3 ≤ j ≤ N (conditioning memory depth number k = 3), etc.By tracking each hazard/failure/risk/damage event, happening sequentially in time, the intention is now to prevent cascading/clustering public health biosystem's inter-correlated exceedances.Since MDOF dynamic environmental process R(t) had been considered to be piecewise ergodic, thus quasi-stationary, probability/risk p k ()≔ Prob{R j >  | R j−1 ≤ , … , R j−k+1 ≤ } for j ≥ k will be also independent of j and solely dependent on conditioning memory depth number k.Thus, non-exceedance (i.e., survival) probability/chances may be approximately assessed, using Poisson's assumption [55][56][57][58][59][60] : Prob(R 1 ≤ ) ≈ 1 being ignored in Equation ( 5) since the chance of the design public health biosystem's failure/hazard/damage probability/risk must be of a low order of magnitude, along with N ≫ k. [61][62][63][64][65] Poisson-type PDF, given by f Poisson (x) = e − P  x P ∕x! with  P being Poisson parameter can be modified following Equation ( 5) with parameter p()N∕T ≈  + () ⋅ T, accounting for clustering, instead of assuming independent temporally successive up-crossing events of the high/critical  levels (in the current study  ≥ 1) can be made.Regarding conditioning memory depth number k, there is a natural way of convergence with  cr being the target critical level/threshold.Note that Equation (5) for k = 1 turns into well-known non-exceedance probability relationship with the corresponding MUR (Mean Up-crossing Rate) function with  + () being MUR of dynamic response level  for the nondimensional public health biosystem's vector R(t), introduced above.[68][69][70][71] Rice's formula is found in Equation ( 7

R).
3][74][75][76][77][78] Equation (7)   relies on Poisson's assumption that separate up-crossing occurrences corresponding to high  levels (in this article,  ≥  cr ) may be assumed nearly independent.Due to intrinsic interdependencies between biocomponents temporally neighbouring out-crossings, the latter may not be true for narrowband bio-processes exhibiting cascading hazards/failures in different dimensions, temporally one after the other.
Given the constructed synthetic vector ⃗ R, these interdependencies form clusters/groups of strongly connected biosystem principal com- As already mentioned, the bio-system's joint quasi-stationarity premise has been used.
9][80][81][82][83][84][85][86][87][88][89] Given the probability of each transient seasonal bio-condition of q m within the nonstationary case's scatter being the same functions as in Equation ( 6), with the exception that p k (, m) corresponds now to a particular short-term seasonal epidemic condition, with the number m.The p k () functions mentioned above are frequently regular in the PDF tail, especially for values  of approaching, and surpassing 1.[81][82][83][84][85] 95% CIs (i.e., confidence intervals) (CI − (), CI + ()), may be estimated empirically from the underlying raw/unfiltered MC simulated/clinically measured dataset.For target levels of  reaching 1, p-% CI of p k () maybe directly represented as having f(p) obtained from the inverse Gaussian-type PDF, having N as a total number of discrete underlying data points.

EXPERIMENT
Making predictions, regarding influenza-like epidemics has long been a focus of epidemiology as well as mathematical biology.Dynamics of public health systems are widely acknowledged to constitute highly nonlinear dynamic systems, spanning over numerous dimensions, yet being spatially cross-correlated.Earlier studies have used a variety of techniques to model the dynamics of influenza-like diseases.
The current section illustrates the efficacy of the Gaidai multivariate risks evaluation methodology, described above using a novel strategy, applied to clinical COVID-19/SARS-COV2 datasets, consisting of daily recorded infected patient time-series, spread over wide terrains.Both COVID-19/SARS-COV2 and influenza are contagious illnesses, that have spread throughout the world with low morbidity and mortality.
Seasonally in the Northern Hemisphere, they occur most commonly in late fall, winter, and early spring, with the winter season seeing their peak occurrence.87][88][89][90][91][92][93] The number of daily new recorded patients is presented in Figure 4A as a synthetic vector ⃗ R made up of combined regional/national daily new patients, counted per million of the relevant region/country's population.

RESULTS AND DISCUSSION
Vector ⃗ R is coalesced from various geographical/national principal components having various epidemic backgrounds.Index j is the running index of the vector ⃗ R. [94][95][96][97][98]  = 1% cut-off value had been used on the horizontal x-axis.Figure 5 shows a forecast of the number of daily new patients, extrapolated following Equation ( 7 Due to occurrence of convergence wrt k, conditioning memory depth number k = 2 had been determined to be enough; see Equation ( 6).The 95% CI in Figure 5 being rather narrow.[101][102][103] The COVID-19/SARS-COV2 infection rates, anticipated for each nation/country over the next 10-100 years have been determined to be less than 5.2%.Typically, influenza-type epidemic thresholds are about 20% of the local population, 2. It should be emphasized that the above-described approach, has the advantages of optimally utilizing measured datasets, handling multidimensionality of public health systems, yet performing accurate extrapolations, based on even limited underlying raw clinical datasets.The predicted non-dimensional level, shown by the blue star in the graph, displays the possibility of epidemic outbreaks in any country within the following decades, see Figure 5.In conclusion, the blue star in Figure 5 indicates the anticipated nondimensional level, which shows the probability of COVID-19/SARS-COV2 outbreaks globally within the coming years.The methodology's

Z
1D system's critical component's global maxima are denoted here as X max T (t), … covering the whole timelapse (0, T).By suitably long (representative) timelapse T, one essentially means a large enough value of T concerning dynamic public health biosystem's autocorrelation and relaxation times. 49-54Let X 1 , … , X N X be environmental public health system key/critical component's local maxima of the critical component process X(t) at discrete instants of time-instants, F I G U R E 2 Map of the world's countries with recorded coronavirus disease 2019/severe acute respiratory syndrome coronavirus 2 (COVID-19/SARS-COV2) cases, 1. temporally increasing, t X 1 < ⋯ < t X N X detected within (0, T).Definitions for the remaining MDOF dynamic public health environmental system's key/critical components,

Figure 3 .
Next, the "scaling" parameter 0 <  ≤ 1 is introduced, to artificially reduce hazard/limit/risk values for all bio-systems nondimensionalized principal components.Public health system's survival chances/probability P() being defined as smooth C 1 function of scaling parameter ; with P ≡ P(1) according to Equation (1).Estimation of the survival (non-exceedance) probability P() F I G U R E 3 Example of how two key components, X and Y, are coalesced into 1 new synthetic vector ⃗ R. Red ellipse marking simultaneous maxima for two different system's bio-components,  cr = 1.
), where .R being the time derivative R ′ (t), and p R .R being the joint PDF (Probability Density Function) for (R,. ), towards epidemic outbreak having a 100-year return period, indicated with a horizontal dotted line, and somewhat beyond.Extrapolated 95% CI is shown by two dotted lines.The goal hazard/failure probability 1 − P from Equation (1) is directly connected to p(), following Equation (5).As a result, it is possible to estimate F I G U R E 4 Daily new recorded patient numbers.(A) vector ⃗ R, scaled following Equation (9) as % of the corresponding country's population.(B) 2D surface versus time, and each country index.bio-system hazard/failure/damage probability/risk 1 − P ≈ 1 − P k ( cr ) following Equation (5).The total number of local maxima within unified synthetic vector ⃗ R was represented by the variable N in Equation (6).

F I G U R E 5 F I G U R E 6
Forecast of daily new patient numbers.The 10-year return level extrapolation of p k () towards the critical level (star) is a % of the local/national population.Extrapolated 95% CI (i.e., confidence interval) indicated with 2 dotted lines.% of the regional/national population on the x-axis.Coronavirus disease 2019/severe acute respiratory syndrome coronavirus 2 (COVID-19/SARS-COV2) world's global statistics, newly registered daily patients from COVID-19/SARS-COV2.SODP 2nd-order plot.Poincare 2nd order plots being SODP (i.e., 2 nd Order Difference Plot).In time series data analysis, SODP offers visualization of sequential differences.

Figure 6
Figure6presents a 2nd-order SODP plot.When employing entropy and AI (i.e., artificial intelligence) pattern identification approach, for example, this sort of visualization helps identify underlying dataset's patterns, to be compared with other relevant clinical datasets.104