Xiaoping Liu

Epidemiological compartmental models, such as SEIR (Susceptible, Exposed, Infectious, and Recovered) models, have been generally used in analyzing epidemiological data and forecasting the trajectory of transmission of infectious diseases such as COVID-19. Experience shows that accurately forecasting the trajectory of COVID-19 transmission curve is a big challenge for researchers in the field of epidemiological modeling because multiple unquantified factors can affect the trajectory of COVID-19 transmission. In the past years, we used a new compartmental model, l-i SEIR model, to analyze the COVID-19 transmission trend in the United States. Unlike the conventional SEIR model and the delayed SEIR model that use or partially use the approximation of temporal homogeneity, the l-i SEIR model takes into account chronological order of infected individuals in both latent (l) period and infectious (i) period, and thus improves the accuracy in forecasting the trajectory of transmission of infectious diseases, especially during periods of rapid rise or fall in the number of infections. This paper describes (1) how to use the new SEIR model (a mechanistic model) combined with fitting methods to simulate or predict trajectory of COVID-19 transmission, (2) how social interventions and new variants of COVID-19 significantly change COVID-19 transmission trends by changing transmission rate coefficient β_n, the fraction of susceptible people (S_n/N), and the reinfection rate, (3) why accurately forecasting COVID-19 transmission trends is difficult, (4) what are the strategies that we have used to improve the forecast outcome and (5) what are some successful examples that we have obtained.

Epidemiological compartmental models, such as SEIR (Susceptible, Exposed, Infectious, and Recovered) models, have been generally used in analyzing epidemiological data and forecasting the trajectory of transmission of infectious diseases such as COVID-19. Experience shows that accurately forecasting the trajectory of COVID-19 transmission curve is a big challenge to researchers in the field of epidemiological modeling. Multiple factors (such as social distancing, vaccinations, public health interventions, and new COVID-19 variants) can affect the trajectory of COVID-19 transmission. In the past years, we used a new compartmental model, l-i SEIR model, to analyze the COVID-19 transmission trend in the United States. The letters l and i are two parameters in the model representing the average time length of the latent period and the average time length of infectious period. The l-i SEIR model takes into account of the temporal heterogeneity of infected individuals and thus improves the accuracy in forecasting the trajectory of transmission of infectious diseases. This paper describes how these multiple factors mentioned above could significantly change COVID-19 transmission trends, why accurately forecasting COVID-19 transmission trend is difficult, what the strategies we have used to improve the forecast outcome, and some of successful examples that we have obtained.

The Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model has been commonly used to analyze the spread of infectious diseases. This 4-compartment (S, E, I and R) model uses an approximation of temporal homogeneity of individuals in these compartments to calculate the transfer rates of the individuals from compartment E to I to R. Although this SEIR model has been generally adopted, the calculation errors caused by temporal homogeneity approximation have not been quantitatively examined. In this study, a 4-compartment l-i SEIR model considering temporal heterogeneity was developed from a previous epidemic model (Liu X., Results Phys. 2021; 20:103712), and a closed-form solution of the l-i SEIR model was derived. Here, l represents the latent period and i represents the infectious period. Comparing l-i SEIR model with the conventional SEIR model, we are able to examine how individuals move through each corresponding compartment in the two SEIR models to find what information may be missed by the conventional SEIR model and what calculation errors may be introduced by using the temporal homogeneity approximation. Simulations showed that l-i SEIR model could generate propagated curves of infectious cases under the condition of l>i. Similar propagated epidemic curves were reported in literature, but the conventional SEIR model could not generate propagated curves under the same conditions. The theoretical analysis showed that the conventional SEIR model overestimates or underestimates the rate at which individuals move from compartment E to I to R in the rising or falling phase of the number of infectious individuals, respectively. Increasing the rate of change in the number of infectious individuals leads to larger calculation errors in the conventional SEIR model. Simulations from the two SEIR models with assumed parameters or with reported daily COVID-19 cases in the United States and in New York further confirmed the conclusions of the theoretical analysis.

The Susceptible-Infectious-Recovered ( SIR ) and SIR derived epidemic models have been commonly used to analyze the spread of infectious diseases. The underlying assumption in these models, such as Susceptible-Exposed-Infectious-Recovered ( SEIR ) model, is that the change in variables E, I or R at time t is dependent on a fraction of E and I at time t . This means that after exposed on a day, this individual may become contagious or even recover on the same day. However, the real situation is different: an exposed individual will become infectious after a latent period ( l ) and then recover after an infectious period ( i ). In this study, we proposed a new SEIR model based on the latent period-infectious period chronological order (Liu X., Results Phys. 2021; 20:103712). An analytical solution to equations of this new SEIR model was derived. From this new SEIR model, we obtained a propagated curve of infectious cases under conditions l > i . Similar propagated epidemic curves were reported in literature. However, the conventional SEIR model failed to simulate the propagated epidemic curves under the same conditions. For l < i , the new SEIR models generated bell-shaped curves for infectious cases, and the curve is near symmetrical to the vertical line passing the curve peak. This characteristic can be found in many epidemic curves of daily COVID-19 cases reported from different countries. However, the curve generated from the conventional SEIR model is a right-skewed bell-shaped curve. An example for applying the analytical solution of the new SEIR model equations to simulate the reported daily COVID-19 cases was also given in this paper.

COVID-19 has killed more than 500,000 people in the United States, as of mid-February 2021. Forecasting of COVID-19 spread is helpful for key policy discussions. The transmission coefficient kn of COVID-19 spread varies across time. Accurately forecasting COVID-19 spread is difficult because of the time-dependent kn and becomes more complicated when coronavirus vaccination needs to be considered. In this study, the l-i AIR model was further developed for analyzing COVID-19 spread accompanied by coronavirus vaccinations in the United States. We determined all values of kn prior to January 13, 2021 and calculated the actual number of cumulative infections (In) including asymptomatic infected individuals. We observed 4 plateaus of kn, which corresponded to four national social events. This suggests that events that reduce social distancing and/or percentage of mask wearing played an important role in the acceleration of COVID-19 transmission. Our simulations show that if the American people return to their normal life before 100 million of people are vaccinated, there is likely to be at least one large surge of daily COVID-19 cases. However, if the American people partially return (kn≤0.4) to normal life after 100 million vaccinations, and completely return (kn=1) to normal life after two thirds of the US population are vaccinated in addition to those who have gained some immunity through coronavirus infections, the US may avoid any additional major surge of COVID-19 cases.

COVID-19 has spread around the world with nearly 360,000 deaths from the virus as of today (5/28/2020). Mathematical models have played an important role in many key policy discussions about COVID-19. SIR or SIR-derived models are a common modeling technique. However, the application of these models needs to solve complicated differential equations, enabling use of these models only by professional researchers. In this study, a simple, SIR-like but individual-based model, the l-i AIR model, is presented. The parameters l and i represent the length of the latent period and the infectious period, respectively. The variable A stands for the number of the infected people in the active infectious period, I for the number of cumulative infected people, and R for the number of the people in recovery or death. The nth terms of the three variables are derived, which can be easily calculated in Microsoft Excel, making the program easy to be used in most offices. A transmission coefficient k and a transient incidence rate a of the infected people are induced in the model to examine the effect of social distancing and the testing capacity of coronavirus on the epidemic curves. The simulated daily new cases from this l-i AIR model can fit very well with the reported daily new cases of COVID-19 in Wuhan, China and in New York City, USA, providing important information about latent period, infectious period and lockdown efficiency, and calculating the number of actual infected people who are positive in antibodies.

Cytoglobin (Cygb), like other members of the globin family, is a nitric oxide (NO) dioxygenase, metabolizing NO in an oxygen (O₂)‐dependent manner. We examined the effect of modification of cysteine sulfhydryl groups of Cygb on its O₂ binding and NO dioxygenase activity. The two cysteine sulfhydryls of Cygb were modified to form either an intramolecular disulfide bond (Cygb_SS), thioether bonds to N‐ethylmaleimide (NEM; Cygb_SC), or were maintained as free SH groups (Cygb_SH). It was observed that the NO dioxygenase activity of Cygb only slightly changed (~ 25%) while the P₅₀ of O₂ binding to Cygb changed over four‐fold with these modifications. Our results suggest that it is possible to separately regulate one Cygb function (such as O₂ binding) without largely affecting the other Cygb functions (such as its NO dioxygenase activity).

The identity of the specific nitric oxide dioxygenase (NOD) that serves as the main in vivo regulator of O₂-dependent NO degradation in smooth muscle remains elusive. Cytoglobin (Cygb) is a recently discovered globin expressed in fibroblasts and smooth muscle cells with unknown function. Cygb, coupled with a cellular reducing system, efficiently regulates the rate of NO consumption by metabolizing NO in an O₂-dependent manner with decreased NO consumption in physiological hypoxia. Here we show that Cygb is a major regulator of NO degradation and cardiovascular tone. Knockout of Cygb greatly prolongs NO decay, increases vascular relaxation, and lowers blood pressure and systemic vascular resistance. We further demonstrate that downregulation of Cygb prevents angiotensin-mediated hypertension. Thus, Cygb has a critical role in the regulation of vascular tone and disease. We suggest that modulation of the expression and NOD activity of Cygb represents a strategy for the treatment of cardiovascular disease.

The Gompertz law of mortality quantitatively describes the mortality rate of humans and almost all multicellular animals. However, its underlying kinetic mechanism is unclear. The Gompertz law cannot explain the effect of temperature on lifespan and the mortality plateau at advanced ages. In this study a reaction kinetics model with a time dependent rate coefficient is proposed to describe the survival and senescence processes. A temperature-dependent mortality function was derived. The new mortality function becomes the Gompertz mortality function with the same relationship of parameters prescribed by the Strehler-Mildvan correlation when age is smaller than a characteristic value {\delta}, and reaches the mortality plateau when age is greater than {\delta}. A closed-form analytical expression for describing the relationship of average lifespan with temperature and other equations are derived from the new mortality function. The derived equations can be used to estimate the limit of average lifespan, predict the maximal longevity, calculate the temperature coefficient of lifespan, and explain the tendency of survival curve. This prediction is consistent with the most recently reported mortality trajectories for single-year birth cohorts. This study suggests that the senescence process results from the imbalance between damaging energy and protecting energy for the critical chemical substance in the body. The rate of senescence of the organism increases while the protecting energy decreases. The mortality plateau is reached when the protecting energy decreases to its minimal levels. The decreasing rate of the protecting energy is temperature-dependent. This study is exploring the connection between biochemical mechanism and demography.