Mathematical prediction of the spreading rate of COVID-19 using entropy-based thermodynamic model

Prediction of the morbidity and mortality rates of COVID-19 in Egypt using non-extensive statistics

Non-extenstive statistics play a significant role in studying the dynamic behaviour of COVID-19 to assist epidemiological scientists to take appropriate decisions about pandemic planning. Generic non-extensive and modified-Tsallis statistics are used to analyze and predict the morbidity and mortality rates in future. The cumulative number of confirmed infection and death in Egypt at interval from 4 March 2020 till 12 April 2022 are analyzed using both non-extensive statistics. Also, the cumulative confirmed data of infection by gender, death by gender, and death by age in Egypt at interval from 4 March 2020 till 29 June 2021 are fitted using both statistics. The best fit parameters are estimated. Also, we study the dependence of the estimated fit parameters on the people gender and age. Using modified-Tsallis statistic, the predictions of the morbidity rate in female is more than the one in male while the mortality rate in male is greater than the one in female. But, within generic non-extensive statistic we notice that the gender has no effect on the rate of infections and deaths in Egypt. Then, we propose expressions for the dependence of the fitted parameters on the age. We conclude that the obtained fit parameters depend mostly on the age and on the type of the statistical approach applied and the mortality risk increased with people aged above 45 years. We predict - using modified-Tsallis - that the rate of infection and death in Egypt will begin to decrease till stopping during the first quarter of 2025.

Systems analysis shows that thermodynamic physiological and pharmacological fundamentals drive COVID-19 and response to treatment

Why a systems analysis view of this pandemic? The current pandemic has inflicted almost unimaginable grief, sorrow, loss, and terror at a global scale. One of the great ironies with the COVID‐19 pandemic, particularly early on, is counter intuitive. The speed at which specialized basic and clinical sciences described the details of the damage to humans in COVID‐19 disease has been impressive. Equally, the development of vaccines in an amazingly short time interval has been extraordinary. However, what has been less well understood has been the fundamental elements that underpin the progression of COVID‐19 in an individual and in populations. We have used systems analysis approaches with human physiology and pharmacology to explore the fundamental underpinnings of COVID‐19 disease. Pharmacology powerfully captures the thermodynamic characteristics of molecular binding with an exogenous entity such as a virus and its consequences on the living processes well described by human physiology. Thus, we have documented the passage of SARS‐CoV‐2 from infection of a single cell to species jump, to tropism, variant emergence and widespread population infection. During the course of this review, the recurrent observation was the efficiency and simplicity of one critical function of this virus. The lethality of SARS‐CoV‐2 is due primarily to its ability to possess and use a variable surface for binding to a specific human target with high affinity. This binding liberates Gibbs free energy (GFE) such that it satisfies the criteria for thermodynamic spontaneity. Its binding is the prelude to human host cellular entry and replication by the appropriation of host cell constituent molecules that have been produced with a prior energy investment by the host cell. It is also a binding that permits viral tropism to lead to high levels of distribution across populations with newly formed virions. This thermodynamic spontaneity is repeated endlessly as infection of a single host cell spreads to bystander cells, to tissues, to humans in close proximity and then to global populations. The principal antagonism of this process comes from SARS‐CoV‐2 itself, with its relentless changing of its viral surface configuration, associated with the inevitable emergence of variants better configured to resist immune sequestration and importantly with a greater affinity for the host target and higher infectivity. The great value of this physiological and pharmacological perspective is that it reveals the fundamental thermodynamic underpinnings of SARS‐CoV‐2 infection.

Non-extensive thermodynamic entropy to predict the dynamics behavior of COVID-19

The current world observations in COVID-19 are hardly tractable as a whole, making situations of information to be incompleteness. In pandemic era, mathematical modeling helps epidemiological scientists to take informing decisions about pandemic planning and predict the disease behavior in the future. In this work, we proposed a non-extensive entropy-based model on the thermodynamic approach for predicting the dynamics of COVID-19 disease. To do so, the epidemic details were considered into a single and time-dependent coefficients model. Their four constraints, including the existence of a maximum point were determined analytically. The model was worked out to give a log-normal distribution for the spread rate using the Tsallis entropy. The width of the distribution function was characterized by maximizing the rate of entropy production. The model predicted the number of daily cases and daily deaths with a fairly good agreement with the World Health Organization (WHO) reported data for world-wide, Iran and China over 2019-2020-time span. The proposed model in this work can be further calibrated to fit on different complex distribution COVID-19 data over different range of times.