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![Approximating the metapopulation of daily incremental COVID‐19 infections with Hubbell's UNTB for metacommunity, implemented with Harris et al. HDP‐MSN model:[7,8] A) with datasets of the USA and B) with datasets of the world.](publication/346261766/figure/fig3/AS:11431281172695633@1688640018992/Approximating-the-metapopulation-of-daily-incremental-COVID-19-infections-with-Hubbells.png)
Approximating the metapopulation of daily incremental COVID‐19 infections with Hubbell's UNTB for metacommunity, implemented with Harris et al. HDP‐MSN model:[7,8] A) with datasets of the USA and B) with datasets of the world.
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Predicting the outbreak risks and/or the inflection (turning or tipping) points of COVID-19 can be rather challenging. Here, it is addressed by modeling and simulation approaches guided by classic ecological theories and by treating the COVID-19 pandemic as a metapopulation dynamics problem. Three classic ecological theories are harnessed, includin...
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Citations
... Both the classes occupy 62.6% of host species and 51% of AGM samples. These same datasets have been analyzed in our previous studies (Ma, 2020a(Ma, , 2020bMa et al., 2022) with different research objectives from this study, and detailed information about these AGM samples can be found in the Supplementary Table S7 of Ma et al. (2022). We further categorize the 4 903 AGM samples into three diet types, including 1 421 carnivores, 1 229 herbivores, and 1 473 omnivores groups, respectively. ...
... Nevertheless, this analogy highlighted their similarity but seemed to ignore their difference. By pointing out this negligence, we do not mean to criticize the notion, and in fact, we have made similar analogies previously in our own publications (Ma, 2020a(Ma, ,2020bMa & Ellison, 2018. In our opinion, except for a handful of exceptions, from academia through societies to many cultures, diversity and heterogeneity are often not rigorously distinguished, if not used interchangeably. ...
... Apart from resilience indicators, some studies investigated the performance of indicators of complexity to anticipate critical transitions [32][33][34]. Complexity indicators measure the system's level of disorder. In the included studies, six indicators of complexity were investigated: Fisher information [32], Kolmogorov complexity and Shannon entropy [34], mutual information, joint counts, and Geary's C coefficient [33] (S1 Table). ...
... Complexity indicators measure the system's level of disorder. In the included studies, six indicators of complexity were investigated: Fisher information [32], Kolmogorov complexity and Shannon entropy [34], mutual information, joint counts, and Geary's C coefficient [33] (S1 Table). In accordance with previous studies, complexity indicators had a lower performance than resilience indicators [18,19], and failed to identify a transition in one study [32]. ...
... In the included studies, six indicators of complexity were investigated: Fisher information [32], Kolmogorov complexity and Shannon entropy [34], mutual information, joint counts, and Geary's C coefficient [33] (S1 Table). In accordance with previous studies, complexity indicators had a lower performance than resilience indicators [18,19], and failed to identify a transition in one study [32]. ...
To reduce the consequences of infectious disease outbreaks, the timely implementation of public health measures is crucial. Currently used early-warning systems are highly context-dependent and require a long phase of model building. A proposed solution to anticipate the onset or termination of an outbreak is the use of so -called resilience indicators. These indicators are based on the generic theory of critical slowing down and require only incidence time series. Here we assess the potential for this approach to contribute to outbreak anticipation. We systematically reviewed studies that used resilience indicators to predict outbreaks or terminations of epidemics. We identified 37 studies meeting the inclusion criteria: 21 using simulated data and 16 real-world data. 36 out of 37 studies detected significant signs of critical slowing down before a critical transition (i.e., the onset or end of an outbreak), with a highly variable sensitivity (i.e., the proportion of true positive outbreak warnings) ranging from 0.03 to 1 and a lead time ranging from 10 days to 68 months. Challenges include low resolution and limited length of time series, a too rapid increase in cases, and strong seasonal patterns which may hamper the sensitivity of resilience indicators. Alternative types of data, such as Google searches or social media data, have the potential to improve predictions in some cases. Resilience indicators may be useful when the risk of disease outbreaks is changing gradually. This may happen, for instance, when pathogens become increasingly adapted to an environment or evolve gradually to escape immunity. High-resolution monitoring is needed to reach sufficient sensitivity. If those conditions are met, resilience indicators could help improve the current practice of prediction, facilitating timely outbreak response. We provide a step-by-step guide on the use of resilience indicators in infectious disease epidemiology, and guidance on the relevant situations to use this approach.
... There are potentially numerous applications of classic ecological theories that can be applied to medical ecology, and the previous introduced ones are those that have formed systematic approaches that are generally applicable to most, if not all, H-MADs. One more ad hoc approach for disease ecology is the applications of previously mentioned TPL, DAR and their integrations in predicting the turning points of COVID-19 infections (Ma, 2020d(Ma, , 2021c. Finally, the previous approaches can be equally applied to study the microbiome-associated animal diseases, although the field seems to have received relatively little attention until today. ...
... A question slightly beyond the scope of this review is what are the significant contributions medical ecology can make to clinic-and biomedicines. Here, we list four fields that medical ecology can support: (1) etiological insights, especially for human microbiome associated diseases (e.g., Li and Ma, 2020d;Ma and Ellison, 2021a); (2) personalized precision medicine (e.g., (3) devising innovative treatment strategies and measures such as the immunotherapy and differential therapy (DTH) of cancers (Adler and Gordon, 2019;Solé and Aguadé-Gorgorió, 2021), and microbiome transplantations; (4) epidemiological forecasting of disease outbreaks and pandemic (e.g., Ma, 2020d). ...
In nature, the interaction between pathogens and their hosts is only one of a handful of interaction relationships between species, including parasitism, predation, competition, symbiosis, commensalism, and among others. From a non-anthropocentric view, parasitism has relatively fewer essential differences from the other relationships; but from an anthropocentric view, parasitism and predation against humans and their well-beings and belongings are frequently related to heinous diseases. Specifically, treating (managing) diseases of humans, crops and forests, pets, livestock, and wildlife constitute the so-termed medical enterprises (sciences and technologies) humans endeavor in biomedicine and clinical medicine, veterinary, plant protection, and wildlife conservation. In recent years, the significance of ecological science to medicines has received rising attentions, and the emergence and pandemic of COVID-19 appear accelerating the trend. The facts that diseases are simply one of the fundamental ecological relationships in nature, and the study of the relationships between species and their environment is a core mission of ecology highlight the critical importance of ecological science. Nevertheless, current studies on the ecology of medical enterprises are highly fragmented. Here, we (i) conceptually overview the fields of disease ecology of wildlife, cancer ecology and evolution, medical ecology of human microbiome-associated diseases and infectious diseases, and integrated pest management of crops and forests, across major medical enterprises. (ii) Explore the necessity and feasibility for a unified medical ecology that spans biomedicine, clinical medicine, veterinary, crop (forest and wildlife) protection, and biodiversity conservation. (iii) Suggest that a unified medical ecology of human diseases is both necessary and feasible, but laissez-faire terminologies in other human medical enterprises may be preferred. (iv) Suggest that the evo-eco paradigm for cancer research can play a similar role of evo-devo in evolutionary developmental biology. (v) Summarized 40 key ecological principles/theories in current disease-, cancer-, and medical-ecology literatures. (vi) Identified key cross-disciplinary discovery fields for medical/disease ecology in coming decade including bioinformatics and computational ecology, single cell ecology, theoretical ecology, complexity science, and the integrated studies of ecology and evolution. Finally, deep understanding of medical ecology is of obvious importance for the safety of human beings and perhaps for all living things on the planet.
... Obviously, masking also belongs to isolation. According to the metapopulation (i.e., population of local populations) theory (Citron et al. 2021, Ma 2020, infectious diseases such as COVID-19 can be modeled as a metapopulation of infectious pathogens, i.e., consisting of many local (regional) populations of pathogens (carried by human hosts) such as the local or regional outbreaks of COVID-19 (e.g., outbreaks in different countries). Also according to classic ecological theories (Hilker et al. 2009, Friedman et al. 2012, Ma 2020, the extinctions of local populations can be common events, although the global metapopulation is usually stable and resilient against global (total) extinction. ...
... According to the metapopulation (i.e., population of local populations) theory (Citron et al. 2021, Ma 2020, infectious diseases such as COVID-19 can be modeled as a metapopulation of infectious pathogens, i.e., consisting of many local (regional) populations of pathogens (carried by human hosts) such as the local or regional outbreaks of COVID-19 (e.g., outbreaks in different countries). Also according to classic ecological theories (Hilker et al. 2009, Friedman et al. 2012, Ma 2020, the extinctions of local populations can be common events, although the global metapopulation is usually stable and resilient against global (total) extinction. Hilker et al. (2009) demonstrated theoretically that the disease dynamics could be rather sensitive to All rights reserved. ...
A bstract
Face masking in current COVID-19 pandemic seems to be a deceivingly simple decision-making problem due to its multifaceted nature. Questions arising from masking span biomedicine, epidemiology, physics, and human behaviors. While science has shown masks work generally, human behaviors (particularly under influences of politics) complicate the problem significantly given science generally assumes rationality and our minds are not always rational and/or honest. Minding minds, a legitimate concern, can also make masking legitimately confusing. To disentangle the potential confusions, particularly, the ramifications of irrationality and dishonesty, here we resort to evolutionary game theory. Specifically, we formulate and analyze the masking problem with a fictitious pair of young lovers, Alice and Bob, as a Sir Philip Sydney (SPS) evolutionary game, inspired by the handicap principle in evolutionary biology and cryptography figures in computer science. With the proposed ABD (Alice and Bob’s dating dilemma) as an asymmetric four-by-four strategic-form game, 16 strategic interactions were identified, and six of which may reach equilibriums with different characteristics such as separating, pooling, and polymorphic hybrid, being Nash, evolutionarily stable or neutrally stable. The six equilibrium types seem to mirror the diverse behaviors of mask believers, skeptics, converted, universal masking, voluntarily masking, coexisted and/or divided world of believers and skeptics. We suggest that the apparently simple ABD game is sufficiently general not only for studying masking policies for populations ( via replicator dynamics), but also for investigating other complex decision-making problems with COVID-19 pandemic including lockdown vs . reopening, herd immunity vs . quarantines, and aggressive tracing vs . privacy protection.
... Similar to SAR/DAR, there is so-called species-time relationship (STR) or diversity-time relationship (DTR) [26]. The PLEC version of DTR was successfully applied to predict the inflection points (tipping points) of COVID-19 infections [28]. ...
... Power law with exponential cutoff, as a variant of PL, has more general applications beyond the abovementioned SAR/DAR/STR/DTR/COVID-19 predictions [25][26][27][28]. PL behaves (grows or declines) exponentially, especially at late stages, and the PLEC possesses an exponential cutoff parameter that ultimately tapers off the unlimited growth or decline ultimately. ...
... As further explained in the next sub-section, the fitting of PLEC can be performed with non-linear optimization, although logtransformed linear fitting, similar to fitting of TPL, can be used. Ma [28] adapted the STR/DTR model to predict the inflection (turning) points of COVID-19, in which maximal accrual or potential diversity is equivalent to maximal infection numbers. In STR/DTR modeling, a convention is to use parameter w in place of the z of SAR/DAR as a diversity-time scaling parameter. ...
Power laws (PLs) have been found to describe a wide variety of natural (physical, biological, astronomic, meteorological, and geological) and man-made (social, financial, and computational) phenomena over a wide range of magnitudes, although their underlying mechanisms are not always clear. In statistics, PL distribution is often found to fit data exceptionally well when the normal (Gaussian) distribution fails. Nevertheless, predicting PL phenomena is notoriously difficult because of some of its idiosyncratic properties, such as lack of well-defined average value and potentially unbounded variance. Taylor's power law (TPL) is a PL first discovered to characterize the spatial and/or temporal distribution of biological populations. It has also been extended to describe the spatiotemporal heterogeneities (distributions) of human microbiomes and other natural and artificial systems, such as fitness distribution in computational (artificial) intelligence. The PL with exponential cutoff (PLEC) is a variant of power-law function that tapers off the exponential growth of power-law function ultimately and can be particularly useful for certain predictive problems, such as biodiversity estimation and turning-point prediction for Coronavirus Diease-2019 (COVID-19) infection/fatality. Here, we propose coupling (integration) of TPL and PLEC to offer a methodology for quantifying the uncertainty in certain estimation (prediction) problems that can be modeled with PLs. The coupling takes advantage of variance prediction using TPL and asymptote estimation using PLEC and delivers CI for the asymptote. We demonstrate the integrated approach to the estimation of potential (dark) biodiversity of the American gut microbiome (AGM) and the turning point of COVID-19 fatality. We expect this integrative approach should have wide applications given duel (contesting) relationship between PL and normal statistical distributions. Compared with the worldwide COVID-19 fatality number on January 24th, 2022 (when this paper is online), the error rate of the prediction with our coupled power laws, made in the May 2021 (based on the fatality data then alone), is approximately 7% only. It also predicted that the turning (inflection) point of the worldwide COVID-19 fatality would not occur until the July of 2022, which contrasts with a recent prediction made by Murray on January 19th of 2022, who suggested that the “end of the pandemic is near” by March 2022.
... Nonetheless, building a predictive model for determining the IP days for visualizing the data on the TBG for countries/regions is a challenge that we encountered. Although many mathematical models have been proposed, [23,24] all of these merely emphasize the model accuracy to epidemic outbreaks instead of the data displays that are easily understood about the IP features on the TBG. ...
Background:
Exponential-like infection growth leading to peaks (denoted by inflection points [IP] or turning points) is usually the hallmark of infectious disease outbreaks, including coronaviruses. To determine the IPs of the novel coronavirus (COVID-19), we applied the item response theory model to detect phase transitions for each country/region and characterize the IP feature on the temporal bar graph (TBG).
Methods:
The IP (using the item difficulty parameter to locate) was verified by the differential equation in calculus and interpreted by the TBG with 2 virtual and real empirical data (i.e., from Collatz conjecture and COVID-19 pandemic in 2020). Comparisons of IPs, R2, and burst strength [BS = ln() denoted by the infection number at IP(Nip) and the item slope parameter(a) in item response theory were made for countries/regions and continents on the choropleth map and the forest plot.
Results:
We found that the evolution of COVID-19 on the TBG makes the data clear and easy to understand, the shorter IP (=53.9) was in China and the longest (=247.3) was in Europe, and the highest R2 (as the variance explained by the model) was in the US, with a mean R2 of 0.98. We successfully estimated the IPs for countries/regions on COVID-19 in 2020 and presented them on the TBG.
Conclusion:
Temporal visualization is recommended for researchers in future relevant studies (e.g., the evolution of keywords in a specific discipline) and is not merely limited to the IP search in COVID-19 pandemics as we did in this study.
... We identify this time scale to be the pandemic inflection time, after which human responses are likely too late to stop the world-wide spread of the disease. Previous studies have discussed an epidemic inflection time [27,28], which corresponds to the time point at which the number of infected people in a population reaches its maximum (i.e. its turning point). This time scale relies on the leveling off of the cumulative number ∫ 0 d ′ ( ′ ) of infections within a relatively short time compared to the global disease transmission time scale. ...
Different virus families, like influenza or corona viruses, exhibit characteristic traits such as typical modes of transmission and replication as well as specific animal reservoirs in which each family of viruses circulate. These traits of genetically related groups of viruses influence how easily an animal virus can adapt to infect humans, how well novel human variants can spread in the population, and the risk of causing a global pandemic. Relating the traits of virus families to their risk of causing future pandemics, and identification of the key time scales within which public health interventions can control the spread of a new virus that could cause a pandemic, are obviously significant. We address these issues using a minimal model whose parameters are related to characteristic traits of different virus families. A key trait of viruses that “spillover” from animal reservoirs to infect humans is their ability to propagate infection through the human population (fitness). We find that the risk of pandemics emerging from virus families characterized by a wide distribution of the fitness of spillover strains is much higher than if such strains were characterized by narrow fitness distributions around the same mean. The dependences of the risk of a pandemic on various model parameters exhibit inflection points. We find that these inflection points define informative thresholds. For example, the inflection point in variation of pandemic risk with time after the spillover represents a threshold time beyond which global interventions would likely be too late to prevent a pandemic.
... Similar to SAR/DAR, there is so-called STR (species-time relationship) or DTR (diversity-time relationship) (Ma 2019). The PLEC version of DTR was successfully applied to predict the inflection points (tipping points) of COVID-19 infections (Ma 2020c). ...
... PLEC, as a variant of power law, has more general applications beyond the above-mentioned SAR/DAR/STR/DTR/COVID-19 predictions (Ma 2018a(Ma , 2018b(Ma , 2019(Ma , 2020c. PL behaves (grows or declines) exponentially, especially at late stages, and the PLEC possesses an exponential-cutoff parameter that ultimately taper off the unlimited growth or decline ultimately. ...
... STR/DTR has the exactly same PL/PLEC models as SAR/DAR described previously, but the data used to fit the models are different and so do the model parameters (Ma 2018b). Ma (2020c) adapted STR/DTR model to predict the inflection points of COVID-19, in which maximal accrual or potential diversity is equivalent to maximal infection numbers. In STR/DTR modeling, a convention is to use parameter w in place of the z of SAR/DAR as diversity-time scaling parameter. ...
Power laws have been found to describe a wide variety of natural (physical, biological, astronomic, meteorological, geological) and man-made (social, financial, computational) phenomena over a wide range of magnitudes, although their underlying mechanisms are not always clear. In statistics, power law distribution is often found to fit data exceptionally well when the normal (Gaussian) distribution fails. Nevertheless, predicting power law phenomena is notoriously difficult because some of its idiosyncratic properties such as lack of well-defined average value, and potentially unbounded variance. TPL (Taylor power law), a power law first discovered to characterize the spatial and/or temporal distribution of biological populations and recently extended to describe the spatiotemporal heterogeneities (distributions) of human microbiomes and other natural and artificial systems such as fitness distribution in computational (artificial) intelligence. The power law with exponential cutoff (PLEC) is a variant of power-law function that tapers off the exponential growth of power-law function ultimately and can be particularly useful for certain predictive problems such as biodiversity estimation and turning-point prediction for COVID-19 infection/fatality. Here, we propose coupling (integration) of TPL and PLEC to offer improved prediction quality of certain power-law phenomena. The coupling takes advantages of variance prediction using TPL and the asymptote estimation using PLEC and delivers confidence interval for the asymptote. We demonstrate the integrated approach to the estimation of potential (dark) biodiversity and turning point of COVID-19 fatality. We expect this integrative approach should have wide applications given the duel relationship between power law and normal statistical distributions.
... In addition, the heterogeneity of the assemblage of species, which falls between single-species population and community, can be measured with the so-termed mixed species population aggregation [11]. Several applications of the TPLE to human microbiome have been reported (e.g., [15][16][17][18]20]). In the present study, we propose and test the application of TPLE for measuring the spatial heterogeneity of human virome. ...
Spatial heterogeneity is a fundamental characteristic of organisms from viruses to humans. Measuring heterogeneity is challenging, especially for naked-eye invisible viruses, but of obvious importance. For example, spatial heterogeneity of virus distribution may strongly influence infection spreading and outbreaks in the case of pathogenic viruses; the spatial distribution (i.e., the inter-subject heterogeneity) of commensal viruses within/on our bodies can influence the competition, coexistence, and dispersal of viruses within or between our bodies. Taylor’s power law (TPL) was first discovered in the 1960s to describe the spatial distributions of plant and/or animal populations, and since then it has been verified by numerous experimental and theoretical studies. Recently, TPL has been extended from population to community level and applied to bacterial communities. Here we report the first comprehensive testing of the TPL fitted to human virome datasets. It was found that the human virome follows the TPL as bacterial communities do. Furthermore, the TPL heterogeneity scaling parameter of human virome is virtually the same as that of the human bacterial microbiome (1.916 vs. 1.926). We postulate that the extreme closeness of human viruses and bacteria in heterogeneity scaling coefficients could be attributed to the fact that most of the viruses that were annotated in this study actually belong to bacteriophages (86% viral OTUs) that “piggyback” on their bacterial hosts, and their distributions are likely host-dependent. The scaling parameter, which measures the inter-subject heterogeneity changes, should be an innate property of human microbiomes including both bacteria and viruses. It is similar to the acceleration coefficient of the gravity (g = 9.8) as specified by Newton’s law, which is invariant on the earth. Nevertheless, we caution that our postulation is contingent on an implicit assumption that the proportion of bacteriophages to total virome may not change significantly when more virus species can be identified in future.
... We identify this time scale to be the pandemic inflection time, after which human responses are likely too late to stop the world-wide spread of the disease. Previous studies have discussed an epidemic inflection time [23,24], which corresponds to the time point at which the number of infected people in a population reaches its maximum (i.e. its turning point). This time scale relies on the leveling off of the cumulative number t 0 dt N (t ) of infections within a relatively short time compared to the global disease transmission time scale. ...
Different virus families, like influenza or corona viruses, exhibit characteristic traits such as typical modes of transmission and replication as well as specific animal reservoirs in which each family of viruses circulate. These traits of genetically related groups of viruses influence how easily an animal virus can adapt to infect humans, how well novel human variants can spread in the population, and the risk of causing a global pandemic. Relating the traits of virus families to their risk of causing future pandemics, and identification of the key time scales within which public health interventions can control the spread of a new virus that could cause a pandemic, are obviously significant. We address these issues using a minimal model whose parameters are related to characteristic traits of different virus families. A key trait of viruses that "spillover" from animal reservoirs to infect humans is their ability to propagate infection through the human population (fitness). We find that the risk of pandemics emerging from virus families characterized by a wide distribution of the fitness of spillover strains is much higher than if such strains were characterized by narrow fitness distributions around the same mean. The dependences of the risk of a pandemic on various model parameters exhibit inflection points. We find that these inflection points define informative thresholds. For example, the inflection point in variation of pandemic risk with time after the spillover represents a threshold time beyond which global interventions would likely be too late to prevent a pandemic.
