Here we propose and implement a generalized mathematical model to find the time evolution of population in infectious diseases and apply the model to study the recent COVID-19 pandemic. Our model at the core is a non-local generalization of the widely used Kermack-McKendrick(KM) model where the susceptible(S) population evolves into two other categories, namely infectives(I) and removed(R). This is the well-known SIR model in which we further divide both S and I into high and low risk categories. We first formulate a set of non-local dynamical equations for the time evolution of distinct population distributions under this categorization in an attempt to describe the general scenario of infectious disease progression. We then solve the non-linear coupled differential equations-(i) numerically by the method of propagation, and (ii) a more flexible and versatile cellular automata (CA) simulation which provides a coarse-grained description of the generalized non-local model. In order to account for multiple factors such as role of spreaders before containment, we introduce a time dependent rate which appears to be essential to explain the sudden spikes before the plateau observed in many cases (for example like China). We demonstrate how this generalized approach allows us to handle the effects of (i) time-dependence of the rate-constants of spread, (ii) different population density, (iii) the age ratio, (iv) quarantine, (v) lockdown, and (vi) social distancing. Our study allows us to make certain predictions regarding the nature of spread with respect to several external parameters, treated as control variables. Analysis of the model clearly shows that due to the strong heterogeneity in the epidemic process originating from the distribution of initial infectives, the theory must be local in character but at the same time connect to a global perspective.
Two factors that are often ignored but could play a crucial role in the progression of an infectious disease are the distributions of inherent susceptibility ($σ_{inh}$) and external infectivity ($ι_{ext}$), in a given population. While the former is determined by the immunity of an individual towards a disease, the latter depends on the duration of exposure to the infection. We model the spatio-temporal propagation of a pandemic using a generalized SIR (Susceptible-Infected-Removed) model by introducing the susceptibility and infectivity distributions to understand their combined effects, whi…
The infection fatality rate (IFR) of the Coronavirus Disease 2019 (COVID-19) is one of the most discussed figures in the context of this pandemic. Using German COVID-19 surveillance data and age-group specific IFR estimates from multiple international studies, this work investigates time-dependent variations in effective IFR over the course of the pandemic. Three different methods for estimating (effective) IFRs are presented: (a) population-averaged IFRs based on the assumption that the infection risk is independent of age and time, (b) effective IFRs based on the assumption that the age dist…
High-throughput molecular screening is required to investigate the origin and diffusion of antimicrobial resistance in pathogen outbreaks. The most frequent cause of human infection is Escherichia coli, which is dominated by sequence type 131 (ST131), a set of rapidly radiating pandemic clones. The highly infectious clades of ST131 originated firstly by a mutation enhancing virulence and adhesion. Secondly, single-nucleotide polymorphisms occurred enabling fluoroquinolone-resistance, which is near-fixed in all ST131. Thirdly, broader resistance through beta-lactamases has been gained and lost …
One clear aspect of behaviour in the COVID-19 pandemic has been people's focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation where people's behaviour is influenced by the current risk of infection and where this behavioural response acts homeostatically to return infection risk to a certain preferred level. This model predicts that the reproduction rate $R$ will be centered around a median value of 1, and that a related measure of relative change in the number of new infections wil…
The effective reproduction number is a key figure to monitor the course of the COVID-19 pandemic. In this study we consider a retrospective modelling approach for estimating the effective reproduction number based on death counts during the first year of the pandemic in Germany. The proposed Bayesian hierarchical model incorporates splines to estimate reproduction numbers flexibly over time while adjusting for varying effective infection fatality rates. The approach also provides estimates of dark figures regarding undetected infections over time. Results for Germany illustrate that estimated …
During a pandemic, there are conflicting demands arising from public health and economic cost. Lockdowns are a common way of containing infections, but they adversely affect the economy. We study the question of how to minimise the economic damage of a lockdown while still containing infections. Our analysis is based on the SIR model, which we analyse using a clock set by the virus. This use of the "virus time" permits a clean mathematical formulation of our problem. We optimise the economic cost for a fixed health cost and arrive at a strategy for navigating the pandemic. This involves adjust…
Mathematical models have come to play a key role in global pandemic preparedness and outbreak response: helping to plan for disease burden, hospital capacity, and inform non-pharmaceutical interventions. Such models have played a pivotal role in the COVID-19 pandemic, with transmission models and, by consequence, modelers guiding global, national, and local responses to SARS-CoV-2. However, these models have systematically failed to account for the social and structural factors which lead to socioeconomic, racial, and geographic health disparities. Why do epidemiologic models of emerging infec…
This work constructs, analyzes, and simulates a new compartmental SEIR-type model for the dynamics and potential control of the current COVID-19 pandemic. The novelty in this work is two-fold. First, the population is divided according to its compliance with disease control directives (lockdown, shelter-in-place, masks/face coverings, physical distancing, etc.) into those who fully comply and those who follow the directives partially, or are necessarily mobile (such as medical staff). This split, indirectly, reflects on the quality and consistency of these measures. This allows the assessment …
A new epidemic model for Covid-19 has been constructed and simulated for eight US states. The coefficients for this model, based on seven coupled differential equations, are carefully evaluated against recorded data on cases and deaths. These projections reveal that Covid-19 will become endemic, spreading for more than two years. If stay-at-home orders are relaxed, most states may experience a secondary peak in 2021. The number of Covid-19 deaths could have been significantly lower in most states that opened up, if lockdowns had been maintained. Additionally, our model predicts that decreasing…
An urgent problem in controlling COVID-19 spreading is to understand the role of undocumented infection. We develop a five-state model for COVID-19, taking into account the unique features of the novel coronavirus, with key parameters determined by the government reports and mathematical optimization. Tests using data from China, South Korea, Italy, and Iran indicate that the model is capable of generating accurate prediction of the daily accumulated number of confirmed cases and is entirely suitable for real-time prediction. The drastically disparate testing and diagnostic standards/policies …
During its first two years, the SARS-CoV-2 pandemic manifested as multiple waves shaped by complex interactions between variants of concern, non-pharmaceutical interventions, and the immunological landscape of the population. Understanding how the age-specific epidemiology of SARS-CoV-2 has evolved throughout the pandemic is crucial for informing policy decisions. We developed an inference-based modelling approach to reconstruct the burden of true infections and hospital admissions in children, adolescents and adults over the seven waves of four variants (wild-type, Alpha, Delta, Omicron BA.1)…
An AI-Enabled Agent-Based Simulation Platform for Studying COVID-19 Pandemic
Johns Hopkins University（约翰斯·霍普金斯大学）；University of Pennsylvania（宾夕法尼亚大学）；ICMR-National Institute for Research in Bacterial Infections（印度医学研究理事会-细菌性疾病研究所）；University of Nebraska-Lincoln（内布拉斯加大学林肯分校）
A mathematical model to calculate the transmissibility of SARS-Cov-2 in Wuhan City was developed and published recently by Tian-Mu Chen et al., Infectious Diseases of Poverty, 2020, https://doi.org/10.1186/s40249-020-00640-3. This paper improves this model in order to study the effect of different scenarios that include actions to contain the pandemic, such as isolation and quarantine of infected and at-risk people. Comparisons made between the different scenarios show that the progress of the infection is found to strongly depend on measures taken in each case. The particular case of Brazil w…
The SARS-CoV-2 pandemic has so far unfolded diversely across the fifty United States of America, reflected both in different time progressions of infection "waves" and in magnitudes of local infection rates. Despite a marked diversity of presentations, most U.S. states experienced their single greatest surge in daily new cases during the transition from Fall 2020 to Winter 2021. Popular media also cite additional similarities between states -- often despite disparities in governmental policies, reported mask-wearing compliance rates, and vaccination percentages. Here, we identify a set of robu…
COVID-19 is now the largest pandemic crisis of this century, with over 16 million registered cases worldwide. African countries have now begun registering an increasing number of cases, yet, not many models developed focus in specific African countries. In our study we use a simple SEIR model to evaluate and predict future scenarios regarding the pandemic crisis in Mozambique. We compare the effect of different policies on the infection curve and estimate epidemiological parameters such as the current infection reproduction number Rt and the growth rate g. We have found a low value for Rt, ran…
More and more countries show a significant slowdown in the number of new COVID-19 infections due to effective governmentally instituted lockdown and social distancing measures. We have analyzed the growth behavior of the top 25 most affected countries by means of a local slope analysis and found three distinct patterns that individual countries follow depending on the strictness of the lockdown protocols: exponential rise and fall, power law, or logistic. For countries showing power law growth we have determined the scaling exponents. For countries that showed a strong slowdown in the rate of …
Epidemic models play a key role in understanding and responding to the emerging COVID-19 pandemic. Widely used compartmental models are static and are of limited use to evaluate intervention strategies with the emerging pandemic. Applying the technology of data assimilation, we propose a Bayesian updating approach for estimating epidemiological parameters using observable information for the purpose of assessing the impacts of different intervention strategies. We adopt a concise renewal model and propose new parameters by disentangling the reduction of instantaneous reproduction number Rt int…
Much traditional statistical modelling assumes that the outcome variables of interest are independent of each other when conditioned on the explanatory variables. This assumption is strongly violated in the case of infectious diseases, particularly in close-contact settings such as households, where each individual's probability of infection is strongly influenced by whether other household members experience infection. On the other hand, general multi-type transmission models of household epidemics quickly become unidentifiable from data as the number of types increases. This has led to a sit…
Phenomenological and deterministic models are often used for the estimation of transmission parameters in an epidemic and for the prediction of its growth trajectory. Such analyses are usually based on single peak outbreak dynamics. In light of the present COVID-19 pandemic, there is a pressing need to better understand observed epidemic growth with multiple peak structures, preferably using first-principles methods. Along the lines of our previous work [Physica A 574, 126014 (2021)], here we apply 2D random-walk Monte Carlo calculations to better understand COVID-19 spread through contact int…
After the first lockdown in response to the COVID-19 outbreak, many countries faced difficulties in balancing infection control with economics. Due to limited prior knowledge, economists began researching this issue using cost-benefit analysis and found that infection control processes significantly affect economic efficiency. A UK study used economic parameters to numerically demonstrate an optimal balance in the process, including keeping the infected population stationary. However, universally applicable knowledge, which is indispensable for the guiding principles of infection control, has …
Epidemiological models with constant parameters may not capture satisfactory infection patterns in the presence of pharmaceutical and non-pharmaceutical mitigation measures during a pandemic, since infectiousness is a function of time. In this paper, an Epidemiology-Informed Neural Network algorithm is introduced to learn the time-varying transmission rate for the COVID-19 pandemic in the presence of various mitigation scenarios. There are asymptomatic infectives, mostly unreported, and the proposed algorithm learns the proportion of the total infective individuals that are asymptomatic infect…
The Influenza Pandemic of 1918-1919, also called Spanish Flu Pandemic, was one of the severest pandemics in history. It is thought that the First World War much influenced the spread of the pandemic. In this paper, we model the pandemic considering both civil and military traffic. We propose a hybrid model to determine how the pandemic spread through the world. Our approach considers both the SEIR-based model for local areas and the network model for global connection between countries. First, we reproduce the situation in 12 countries. Then, we simulate another scenario: there was no military…
An investigation was conducted to study the robustness of the results obtained from the cellular automata model which describes the spread of the HIV infection within lymphoid tissues [R. M. Zorzenon dos Santos and S. Coutinho, Phys. Rev. Lett. 87, 168102 (2001)]. The analysis focussed on the dynamic behavior of the model when defined in lattices with different symmetries and dimensionalities. The results illustrated that the three-phase dynamics of the planar models suffered minor changes in relation to lattice symmetry variations and, while differences were observed regarding dimensionality …
The spread of COVID-19 during the initial phase of the first half of 2020 was curtailed to a larger or lesser extent through measures of social distancing imposed by most countries. In this work, we link directly, through machine learning techniques, infection data at a country level to a single number that signifies social distancing effectiveness. We assume that the standard SIR model gives a reasonable description of the dynamics of spreading, and thus the social distancing aspect can be modeled through time-dependent infection rates that are imposed externally. We use an exponential ansatz…
Understanding how widely COVID-19 has spread is critical for examining the pandemic's progression. Despite efforts to carefully monitor the pandemic, the number of confirmed cases may underestimate the total number of infections. We introduce a demographic scaling model to estimate COVID-19 infections using an broadly applicable approach that is based on minimal data requirements: COVID-19 related deaths, infection fatality rates (IFRs), and life tables. As many countries lack reliable estimates of age-specific IFRs, we scale IFRs between countries using remaining life expectancy as a marker t…
The results of Kermack-McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of epidemic, systematically. The basic goal is to capture the effects of spreading of infection over a scale of length. This CA model can provide the rate of growth of the infection over the space which was lacking in the mean-field like SIR model. The motion of the circular front of an infected cluster shows a linear behaviour in time. The correlation of a particular site to be infected, with respect to the central site is also stu…
The COVID-19 pandemic has posed a policy making crisis where efforts to slow down or end the pandemic conflict with economic priorities. This paper provides mathematical analysis of optimal disease control policies with idealized compartmental models for disease propagation and simplistic models of social and economic costs. Two locally optimal control strategies are found and categorized as `suppression' and `mitigation' strategies. We analyze how these strategies change when we incorporate vaccination into the model and find a new optimal `delay-mitigation' strategy.
Cities become mission-critical zones during pandemics and it is vital to develop a better understanding of the factors that are associated with infection levels. The COVID-19 pandemic has impacted many cities severely; however, there is significant variance in its impact across cities. Pandemic infection levels are associated with inherent features of cities (e.g., population size, density, mobility patterns, socioeconomic condition, and health environment), which need to be better understood. Intuitively, the infection levels are expected to be higher in big urban agglomerations, but the meas…
A simple analytical model for modeling the evolution of the 2020 COVID-19 pandemic is presented. The model is based on the numerical solution of the widely used Susceptible-Infectious-Removed (SIR) populations model for describing epidemics. We consider an expanded version of the original Kermack-McKendrick model, which includes a decaying value of the parameter $β$ (the effective contact rate) due to externally imposed conditions, to which we refer as the forced-SIR (FSIR) model. We introduce an approximate analytical solution to the differential equations that represent the FSIR model which …
We model and forecast the early evolution of the COVID-19 pandemic in Brazil using Brazilian recent data from February 25, 2020 to March 30, 2020. This early period accounts for unawareness of the epidemiological characteristics of the disease in a new territory, sub-notification of the real numbers of infected people and the timely introduction of social distancing policies to flatten the spread of the disease. We use two variations of the SIR model and we include a parameter that comprises the effects of social distancing measures. Short and long term forecasts show that the social distancin…
COVID-19 pandemic is one of the major disasters that humanity has ever faced. In this paper, we try to model the effect of vaccination in controlling the pandemic, particularly in context to the third wave which is predicted to hit globally. Here we have modified the SEIRD model by introducing a vaccination term. One of our main assumptions is that the infection rate (\b{eta}(t)) is oscillatory. This oscillatory nature has been discussed earlier in literature with reference to the seasonality of epidemics. However, in our case we invoke this nature of the infection rate (\b{eta}(t)) to model t…
A model of reactive social distancing in epidemics is proposed, in which the infection rate changes with the number infected. The final-size equation for the total number that the epidemic will infect can be derived analytically, as can the peak infection proportion. This model could assist planners during for example the COVID-19 pandemic.
The slogan "nobody is safe until everybody is safe" is a dictum to raise awareness that in an interconnected world, pandemics such as COVID-19, require a global approach. Motivated by the ongoing COVID-19 pandemic, we model here the spread of a virus in interconnected communities and explore different vaccination scenarios, assuming that the efficacy of the vaccination wanes over time. We start with susceptible populations and consider a susceptible-vaccinated-infected-recovered model with unvaccinated ("Bronze"), moderately vaccinated ("Silver") and very well vaccinated ("Gold") communities, …
The new coronavirus known as COVID-19 is spread world-wide since December 2019. Without any vaccination or medicine, the means of controlling it are limited to quarantine and social distancing. Here we study the spatio-temporal propagation of the first wave of the COVID-19 virus in China and compare it to other global locations. We provide a comprehensive picture of the spatial propagation from Hubei to other provinces in China in terms of distance, population size, and human mobility and their scaling relations. Since strict quarantine has been usually applied between cities, more insight abo…
University of Cambridge（剑桥大学）；UNC-Chapel Hill（北卡罗来纳大学教堂山分校）；UNC Gilling School of Global Public Health（北卡罗来纳大学吉林斯全球公共卫生学院）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；University of Toronto（多伦多大学）；Canadian Institute for Advanced Research（加拿大高等研究院）；California State University Fullerton（加州州立大学富勒顿分校）；Oberlin College（欧柏林学院）
We present a new mathematical model to explicitly capture the effects that the three restriction measures: the lockdown date and duration, social distancing and masks, and, schools and border closing, have in controlling the spread of COVID-19 infections $i(r, t)$. Before restrictions were introduced, the random spread of infections as described by the SEIR model grew exponentially. The addition of control measures introduces a mixing of order and disorder in the system's evolution which fall under a different mathematical class of models that can eventually lead to critical phenomena. A gener…
The COVID-19 pandemic has severely impacted health systems and economies worldwide. Significant global efforts are therefore ongoing to improve vaccine efficacies, optimize vaccine deployment, and develop new antiviral therapies to combat the pandemic. Mechanistic viral dynamics and quantitative systems pharmacology models of SARS-CoV-2 infection, vaccines, immunomodulatory agents, and antiviral therapeutics have played a key role in advancing our understanding of SARS-CoV-2 pathogenesis and transmission, the interplay between innate and adaptive immunity to influence the outcomes of infection…
The COVID-19 pandemic has affected all countries of the world producing a substantial number of fatalities accompanied by a major disruption in their social, financial, and educational organization. The strict disciplinary measures implemented by China were very effective and thus were subsequently adopted by most world countries to various degrees. The infection duration and number of infected persons are of critical importance for the battle against the pandemic. We use the quantitative landscape of the disease spreading in China as a benchmark and utilize infection data from eight countries…
Analyzing the SARS-CoV-2 pandemic outbreak based on actual data while reflecting the characteristics of the real city provides beneficial information for taking reasonable infection control measures in the future. We demonstrate agent-based modeling for Tokyo based on GPS information and official national statistics and perform a spatiotemporal analysis of the infection situation in Tokyo. As a result of the simulation during the first wave of SARS-CoV-2 in Tokyo using real GPS data, the infection occurred in the service industry, such as restaurants, in the city center, and then the infected …
Covid-19 is raging a devastating trail with the highest mortality-to-infected ratio ever for a pandemic. Lack of vaccine and therapeutic has rendered social exclusion through lockdown as the singular mode of containment. Harnessing the predictive powers of Machine Learning within a 6 dimensional infection kinetic model, depicting interactive evolution of 6 infection stages - healthy susceptible ($H$), predisposed comorbid susceptible ($P$), infected ($I$), recovered ($R$), herd immunized ($V$) and mortality ($D$) - the model, PHIRVD, provides the first accurate mortality prediction of 18 count…
Countries highly exposed to incoming traffic from China were expected to be at the highest risk of COVID-19 spread. However, COVID-19 case numbers (infection levels) are negatively correlated with incoming traffic-level. Moreover, infection levels are positively correlated with population-size, while the latter should only affect infection-level once herd immunity is reached. These could be explained if a low-virulence strain (LVS) began spreading a few months earlier from China, providing immunity from the later emerging known SARS-CoV-2 high-virulence strain (HVS). We find that the dynamics …
We show that the COVID-19 pandemic under social distancing exhibits universal dynamics. The cumulative numbers of both infections and deaths quickly cross over from exponential growth at early times to a longer period of power law growth, before eventually slowing. In agreement with a recent statistical forecasting model by the IHME, we show that this dynamics is well described by the erf function. Using this functional form, we perform a data collapse across countries and US states with very different population characteristics and social distancing policies, confirming the universal behavior…
Stanford University（斯坦福大学）；National University of Singapore（新加坡国立大学）；Imperial College London（帝国理工学院）
Since COVID-19 vaccines became available, no studies have quantified how different disaster evacuation strategies can mitigate pandemic risks in shelters. Therefore, we applied an age-structured epidemiological model, known as the Susceptible-Exposed-Infectious-Recovered (SEIR) model, to investigate to what extent different vaccine uptake levels and the Diversion protocol implemented in Taiwan decrease infections and delay pandemic peak occurrences. Taiwan's Diversion protocol involves diverting those in self-quarantine due to exposure, thus preventing them from mingling with the general publi…
Coronavirus disease (COVID-19) which is caused by SARS-COV2 has become a pandemic. This disease is highly infectious and potentially fatal, causing a global public health concern. To contain the spread of COVID-19, governments are adopting nationwide interventions, like lockdown, containment and quarantine, restrictions on travel, cancelling social events and extensive testing. To understand the effects of these measures on the control of the epidemic in a data-driven manner, we propose a probabilistic cellular automata (PCA) based modified SEIQR model. The transitions associated with the mode…
Extreme public health interventions play a critical role in mitigating the local and global prevalence and pandemic potential of COVID-19. Here, we use population size for pathogen transmission to measure the intensity of public health interventions, which is a key characteristic variable for nowcasting and forecasting of the epidemic. By formulating a hidden Markov dynamic system and using nonlinear filtering theory, we have developed a stochastic epidemic dynamic model under public health interventions. The model parameters and states are estimated in time from internationally available publ…
In this work, we simulate the COVID-19 pandemic dynamics in a population modeled as a network of groups wherein infection can propagate both via intra-group and via inter-group interactions. Our results emphasize the importance of diminishing the inter-group infections in the effort of substantial flattening and delaying of the epi(demiologic) curve with concomitant mitigation of disastrous economy and social consequences. To exemplify with a limiting case, splitting a population into m (say, 5 or 10) noninteracting groups while keeping intra-group interaction unchanged yields a stretched epid…
One of the central tools to control the COVID-19 pandemics is the knowledge of its spreading dynamics. Here we develop a fractal model capable of describe this dynamics, in term of daily new cases, and provide quantitative criteria for some predictions. We propose a fractal dynamical model using conformed derivative and fractal time scale. A Burr-XII shaped solution of the fractal-like equation is obtained. The model is tested using data from several countries, showing that a single function is able to describe very different shapes of the outbreak. The diverse behavior of the outbreak on thos…
Lockdown procedures have been proven successful in mitigating the spread of the viruses in this COVID-19 pandemic, but they also have devastating impact on the economy. We use a modified Susceptible-Infectious-Recovered-Deceased model with time dependent infection rate to simulate how the infection is spread under lockdown. The economic cost due to the loss of workforce and incurred medical expenses is evaluated with a simple model. We find the best strategy, meaning the smallest economic cost for the entire course of the pandemic, is to keep the strict lockdown as long as possible.
A well-known characteristic of pandemics such as COVID-19 is the high level of transmission heterogeneity in the infection spread: not all infected individuals spread the disease at the same rate and some individuals (superspreaders) are responsible for most of the infections. To quantify this phenomenon requires the analysis of the effect of the variance and higher moments of the infection distribution. Working in the framework of stochastic branching processes, we derive an approximate analytical formula for the probability of an outbreak in the high variance regime of the infection distribu…
The classic SIR model of epidemic dynamics is solved completely by quadratures, including a time integral transform expanded in a series of incomplete gamma functions. The model is also generalized to arbitrary time-dependent infection rates and solved explicitly when the control parameter depends on the accumulated infections at time $t$. Numerical results are presented by way of comparison. Autonomous and non-autonomous generalizations of SIR for interacting regions are also considered, including non-separability for two or more interacting regions. A reduction of simple SIR models to one va…
We analyse the temporal and regional structure in mortality rates related to COVID-19 infections. We relate the fatality date of each deceased patient to the corresponding day of registration of the infection, leading to a nowcasting model which allows us to estimate the number of present-day infections that will, at a later date, prove to be fatal. The numbers are broken down to the district level in Germany. Given that death counts generally provide more reliable information on the spread of the disease compared to infection counts, which inevitably depend on testing strategy and capacity, t…
Epidemiological models are the mathematical models that capture the dynamics of epidemics. The spread of the virus has two routes - exogenous and endogenous. The exogenous spread is from outside the population under study, and endogenous spread is within the population under study. Although some of the models consider the exogenous source of infection, they have not studied the interplay between exogenous and endogenous spreads. In this paper, we introduce a novel model - the Exo-SIR model that captures both the exogenous and endogenous spread of the virus. We analyze to find out the relations…
We propose a time-parameterized analogy between the thermodynamic behavior of a 3-level energy system and the progression of the HIV infection described by the cell population evolution generated by an appropriated cellular automata model. The development of internal energy and its fluctuations, and of the entropy of the 3-level energy system allows the identification of an effective temperature that uniquely characterizes the three main stages of the dynamic process of HIV infection. Furthermore, this thermodynamical equivalence allows obtaining the instants associated with particular time in…
The COVID-19 pandemic has posed significant challenges in modeling its complex epidemic transmissions, infection and contagion, which are very different from known epidemics. The challenges in quantifying COVID-19 complexities include effectively modeling its process and data uncertainties. The uncertainties are embedded in implicit and high-proportional undocumented infections, asymptomatic contagion, social reinforcement of infections, and various quality issues in the reported data. These uncertainties become even more apparent in the first two months of the COVID-19 pandemic, when the rele…
COVID-19--a viral infectious disease--has quickly emerged as a global pandemic infecting millions of people with a significant number of deaths across the globe. The symptoms of this disease vary widely. Depending on the symptoms an infected person is broadly classified into two categories namely, asymptomatic and symptomatic. Asymptomatic individuals display mild or no symptoms but continue to transmit the infection to otherwise healthy individuals. This particular aspect of asymptomatic infection poses a major obstacle in managing and controlling the transmission of the infectious disease. I…
We present a robust data-driven machine learning analysis of the COVID-19 pandemic from its early infection dynamics, specifically infection counts over time. The goal is to extract actionable public health insights. These insights include the infectious force, the rate of a mild infection becoming serious, estimates for asymtomatic infections and predictions of new infections over time. We focus on USA data starting from the first confirmed infection on January 20 2020. Our methods reveal significant asymptomatic (hidden) infection, a lag of about 10 days, and we quantitatively confirm that t…
Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend ma…
