Heterogeneity versus the COVID-19 Pandemic

In this paper, heterogeneity is formally defined, and its properties are explored. We define and distinguish observable versus non-observable heterogeneity. It is proposed that heterogeneity among the vulnerable is a significant factor in the contagion impact of COVID-19, as demonstrated with incidence rates on a Diamond Princess Cruise ship in February 2020. Given the nature of the disease, its heterogeneity and human social norms, pre-voyage and post-voyage quick testing procedures may become the new standard for cruise ship passengers and crew. The technological advances in testing available today would facilitate more humanistic treatment as compared to more archaic quarantine and isolation practices for all onboard ship. With quick testing, identification of those infected and thus not allowed to embark on a cruise or quarantining those disembarking and other mitigation strategies, the popular cruise adventure could be available safely again. Whatever the procedures implemented, the methodological purpose of this study should add valuable insight in the modeling of disease and specifically, the COVID-19 virus.

99 what are the differences? A literature search in epidemiology and/or biostatistics offers no help to prove 100 either the existence or absence of binomial heterogeneity in the data for or in Table 1. Hence, we 101 continue probing matters with respect to heterogeneity.

102
The concept of heterogeneity seems to have escaped the researchers and epidemiologists' scrutiny 103 for a long time. It is time well spent and worthwhile to revive an interest in the construct of 104 heterogeneity, and that is exactly what this article is trying to accomplish. Hence, we first define and 105 construct an approach for the idea of heterogeneity. To be specific, we first discuss Poisson 106 heterogeneity and then take up binomial heterogeneity. Maybe our research direction about 107 heterogeneity is, perhaps, pioneering. However, we believe that our approach is easily extendable for 108 many other similar methodological setups. We illustrate our definition and all derived expressions for 109 heterogeneity using COVID-19's data pertaining to the Diamond Princess Cruise ship, Yokohama, 2020 110 as displayed in Table 1. 141 It is reasonable to imagine that the prevalence levels follow a conjugate, stochastic gamma distribution.
142 The so-called conjugate prior knowledge in the Bayesian framework smooths the statistical analytic 143 process. It is known that the conjugate prior for the Poisson distribution is gamma, whose pdf is 214 we obtained the non-observable heterogeneity and displayed in 236 Likewise, using the expression 237 , (9), 238 we estimated the odds for a COVID-19 case to become a symptomatic case as shown in Table 2. Notice 239 that both odds ( and ) are low but their odds ratio, 240 (10) 241 is not negligible but reveals that the situation is favorable to symptomatic rather than asymptomatic.
242 This discovery is feasible because of the approach, and it is an eye-opening reality for the medical 243 professionals in their desire to control the spread of the COVID-19 virus. Both the observable, and 244 non-observable, binomial heterogeneity (see their values in Table 3) were decreasing for the 245 number, of asymptomatic COVID-19 cases. The distance, between the observable and non-246 observable for asymptomatic cases was moderate in the beginning, then increased, and then decreased 247 over the next days (see their values in Table 3). However, the distance, between the observable, 248 of the asymptomatic cases and the observable, of the symptomatic cases was narrow, then wider, 249 and then moderate over the days (their values in Table 3).

250
For a COVID-19 case to become a symptomatic type, the chance is moderate to less and then more 251 over the days ( in Table 3). The estimate of the shape and scale parameter happened to be and 252 respectively (see their values in Table 3). Both the shape parameter and the scale parameter values 253 decreased drastically over the days. From the p-values in Table 4, we infer that the prevalence rate, , 254 the distances, , and do differ significantly over the three groups of dyad days.
255 The chance for COVID-19 to become an asymptomatic type does not differ significantly across the three 256 groups. On the contrary, the non-observable heterogeneities of the Poisson random number, and 427 The configuration of the distance, between the observable and non-observable in Poisson 428 mechanism. We now turn to discuss stochastic properties of the Poisson distribution are given in Figure   429 3.  The conditional variability of is a percent of its expected number , implying 480 that it exhibits under dispersion. Likewise, the conditional variability of is a percent of its  portrays the drift between the symptomatic 500 observable, and the asymptomatic observable, and it is simplified to this function 501 (see Table 3 for their values), due to applying 502 .