Parameter identification for a stochastic SEIRS epidemic model: case study influenza

Kalman Filter-Based Epidemiological Model for Post-COVID-19 Era Surveillance and Prediction

In the post-COVID-19 era, the dynamic spread of COVID-19 poses new challenges to epidemiological modelling, particularly due to the absence of large-scale screening and the growing complexity introduced by immune failure and reinfections. This paper proposes an AEIHD (antibody-acquired, exposed, infected, hospitalised, and deceased) model to analyse and predict COVID-19 transmission dynamics in the post-COVID-19 era. This model removes the susceptible compartment and combines the recovered and vaccinated compartments into an "antibody-acquired" compartment. It also introduces a new hospitalised compartment to monitor severe cases. The model incorporates an antibody-acquired infection rate to account for immune failure. The Extended Kalman Filter based on the AEIHD model is proposed for real-time state and parameter estimation, overcoming the limitations of fixed-parameter approaches and enhancing adaptability to nonlinear dynamics. Simulation studies based on reported data from Australia validate the AEIHD model, demonstrating its capability to accurately capture COVID-19 transmission dynamics with limited statistical information. The proposed approach addresses the key limitations of traditional SIR and SEIR models by integrating hospitalisation data and time-varying parameters, offering a robust framework for monitoring and predicting epidemic behaviours in the post-COVID-19 era. It also provides a valuable tool for public health decision-making and resource allocation to handle rapidly evolving epidemiology.

Economical-epidemiological analysis of the coffee trees rust pandemic

Coffee leaf rust is a prevalent botanical disease that causes a worldwide reduction in coffee supply and its quality, leading to immense economic losses. While several pandemic intervention policies (PIPs) for tackling this rust pandemic are commercially available, they seem to provide only partial epidemiological relief for farmers. In this work, we develop a high-resolution spatiotemporal economical-epidemiological model, extending the Susceptible-Infected-Removed model, that captures the rust pandemic's spread in coffee tree farms and its associated economic impact. Through extensive simulations for the case of Colombia, a country that consists mostly of small-size coffee farms and is the second-largest coffee producer in the world, our results show that it is economically impractical to sustain any profit without directly tackling the rust pandemic. Furthermore, even in the hypothetical case where farmers perfectly know their farm's epidemiological state and the weather in advance, any rust pandemic-related efforts can only amount to a limited profit of roughly 4% on investment. In the more realistic case, any rust pandemic-related efforts are expected to result in economic losses, indicating that major disturbances in the coffee market are anticipated.

Modeling correlated uncertainties in stochastic compartmental models

We consider compartmental models of communicable disease with uncertain contact rates. Stochastic fluctuations are often added to the contact rate to account for uncertainties. White noise, which is the typical choice for the fluctuations, leads to significant underestimation of the disease severity. Here, starting from reasonable assumptions on the social behavior of individuals, we model the contacts as a Markov process which takes into account the temporal correlations present in human social activities. Consequently, we show that the mean-reverting Ornstein-Uhlenbeck (OU) process is the correct model for the stochastic contact rate. We demonstrate the implication of our model on two examples: a Susceptibles-Infected-Susceptibles (SIS) model and a Susceptibles-Exposed-Infected-Removed (SEIR) model of the COVID-19 pandemic and compare the results to the available US data from the Johns Hopkins University database. In particular, we observe that both compartmental models with white noise uncertainties undergo transitions that lead to the systematic underestimation of the spread of the disease. In contrast, modeling the contact rate with the OU process significantly hinders such unrealistic noise-induced transitions. For the SIS model, we derive its stationary probability density analytically, for both white and correlated noise. This allows us to give a complete description of the model's asymptotic behavior as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the SEIR model, where the probability density is not available in closed form, we study the transitions using Monte Carlo simulations. Our modeling approach can be used to quantify uncertain parameters in a broad range of biological systems.

Tumor growth and population modeling in a toxicant-stressed random environment

When examining some factors that contribute to the growth or decline of a population or tumor, it is essential to consider a random hypothesis. By analyzing the effects of stress on a population (or volume of tumor growth) in a random environment, we develop stochastic models describing the dynamics of the population (or tumor growth) based on random adjustments to the population's intrinsic growth rate, carrying capacity, and harvesting efforts (or tumor treatments). Apart from the models' ability to capture fluctuations, the availability of a shape parameter in the models gives it the flexibility to describe a variety of population/tumor data with different shapes. The distribution of the stressed population size with or without harvesting (or treatments) is derived and used to calculate the maximum expected amount of harvests that can be taken from the population without depleting resources in the long run (or the minimum amount of chemotherapy needed to cause shrinkage or eradication of a tumor). The work done is applied to analyze tumor growth using published data comprising of the volume of breast tumor obtained by orthotopically implanting LM2-[Formula: see text] cells into the right inguinal mammary fat pads of 6- to 8-week-old female Severe Combined Immuno-Deficient mice.

Epicasting: An Ensemble Wavelet Neural Network for forecasting epidemics

Infectious diseases remain among the top contributors to human illness and death worldwide, among which many diseases produce epidemic waves of infection. The lack of specific drugs and ready-to-use vaccines to prevent most of these epidemics worsens the situation. These force public health officials and policymakers to rely on early warning systems generated by accurate and reliable epidemic forecasters. Accurate forecasts of epidemics can assist stakeholders in tailoring countermeasures, such as vaccination campaigns, staff scheduling, and resource allocation, to the situation at hand, which could translate to reductions in the impact of a disease. Unfortunately, most of these past epidemics exhibit nonlinear and non-stationary characteristics due to their spreading fluctuations based on seasonal-dependent variability and the nature of these epidemics. We analyze various epidemic time series datasets using a maximal overlap discrete wavelet transform (MODWT) based autoregressive neural network and call it Ensemble Wavelet Neural Network (EWNet) model. MODWT techniques effectively characterize non-stationary behavior and seasonal dependencies in the epidemic time series and improve the nonlinear forecasting scheme of the autoregressive neural network in the proposed ensemble wavelet network framework. From a nonlinear time series viewpoint, we explore the asymptotic stationarity of the proposed EWNet model to show the asymptotic behavior of the associated Markov Chain. We also theoretically investigate the effect of learning stability and the choice of hidden neurons in the proposal. From a practical perspective, we compare our proposed EWNet framework with twenty-two statistical, machine learning, and deep learning models for fifteen real-world epidemic datasets with three test horizons using four key performance indicators. Experimental results show that the proposed EWNet is highly competitive compared to the state-of-the-art epidemic forecasting methods.

Global analysis and prediction scenario of infectious outbreaks by recurrent dynamic model and machine learning models: A case study on COVID-19

It is essential to evaluate patient outcomes at an early stage when dealing with a pandemic to provide optimal clinical care and resource management. Many methods have been proposed to provide a roadmap against different pandemics, including the recent pandemic disease COVID-19. Due to recurrent epidemic waves of COVID-19, which have been observed in many countries, mathematical modeling and forecasting of COVID-19 are still necessary as long as the world continues to battle against the pandemic. Modeling may aid in determining which interventions to try or predict future growth patterns. In this article, we design a combined approach for analyzing any pandemic in two separate parts. In the first part of the paper, we develop a recurrent SEIRS compartmental model to predict recurrent outbreak patterns of diseases. Due to its time-varying parameters, our model is able to reflect the dynamics of infectious diseases, and to measure the effectiveness of the restrictive measures. We discuss the stable solutions of the corresponding autonomous system with frozen parameters. We focus on the regime shifts and tipping points; then we investigate tipping phenomena due to parameter drifts in our time-varying parameters model that exhibits a bifurcation in the frozen-in case. Furthermore, we propose an optimal numerical design for estimating the system’s parameters. In the second part, we introduce machine learning models to strengthen the methodology of our paper in data analysis, particularly for prediction scenarios. We use MLP, RBF, LSTM, ANFIS, and GRNN for training and evaluation of COVID-19. Then, we compare the results with the recurrent dynamical system in the fitting process and prediction scenario. We also confirm results by implementing our methods on the released data on COVID-19 by WHO for Italy, Germany, Iran, and South Africa between 1/22/2020 and 7/24/2021, when people were engaged with different variants including Alpha, Beta, Gamma, and Delta. The results of this article show that the dynamic model is adequate for long-term analysis and data fitting, as well as obtaining parameters affecting the epidemic. However, it is ineffective in providing a long-term forecast. In contrast machine learning methods effectively provide disease prediction, although they do not provide analysis such as dynamic models. Finally, some metrics, including RMSE, R-Squared, and accuracy, are used to evaluate the machine learning models. These metrics confirm that ANFIS and RBF perform better than other methods in training and testing zones.

Stochastic Modeling and Forecasting of Covid-19 Deaths: Analysis for the Fifty States in the United States

In this work, we study and analyze the aggregate death counts of COVID-19 reported by the United States Centers for Disease Control and Prevention (CDC) for the fifty states in the United States. To do this, we derive a stochastic model describing the cumulative number of deaths reported daily by CDC from the first time Covid-19 death is recorded to June 20, 2021 in the United States, and provide a forecast for the death cases. The stochastic model derived in this work performs better than existing deterministic logistic models because it is able to capture irregularities in the sample path of the aggregate death counts. The probability distribution of the aggregate death counts is derived, analyzed, and used to estimate the count’s per capita initial growth rate, carrying capacity, and the expected value for each given day as at the time this research is conducted. Using this distribution, we estimate the expected first passage time when the aggregate death count is slowing down. Our result shows that the expected aggregate death count is slowing down in all states as at the time this analysis is conducted (June 2021). A formula for predicting the end of Covid-19 deaths is derived. The daily expected death count for each states is plotted as a function of time. The probability density function for the current day, together with the forecast and its confidence interval for the next four days, and the root mean square error for our simulation results are estimated.

State-controlled epidemic in a game against a novel pathogen

The pandemic reminded us that the pathogen evolution still has a serious effect on human societies. States, however, can prepare themselves for the emergence of a novel pathogen with unknown characteristics by analysing potential scenarios. Game theory offers such an appropriate tool. In our game-theoretical framework, the state is playing against a pathogen by introducing non-pharmaceutical interventions to fulfil its socio-political goals, such as guaranteeing hospital care to all needed patients, keeping the country functioning, while the applied social restrictions should be as soft as possible. With the inclusion of activity and economic sector dependent transmission rate, optimal control of lockdowns and health care capacity management is calculated. We identify the presence and length of a pre-symptomatic infectious stage of the disease to have the greatest effect on the probability to cause a pandemic. Here we show that contrary to intuition, the state should not strive for the great expansion of its health care capacities even if its goal is to provide care for all requiring it and minimize the cost of lockdowns.

Analysis of multi-strain infection of vaccinated and recovered population through epidemic model: Application to COVID-19

In this work, an innovative multi-strain SV EAIR epidemic model is developed for the study of the spread of a multi-strain infectious disease in a population infected by mutations of the disease. The population is assumed to be completely susceptible to n different variants of the disease, and those who are vaccinated and recovered from a specific strain k (k ≤ n) are immune to previous and present strains j = 1, 2, ⋯, k, but can still be infected by newer emerging strains j = k + 1, k + 2, ⋯, n. The model is designed to simulate the emergence and dissemination of viral strains. All the equilibrium points of the system are calculated and the conditions for existence and global stability of these points are investigated and used to answer the question as to whether it is possible for the population to have an endemic with more than one strain. An interesting result that shows that a strain with a reproduction number greater than one can still die out on the long run if a newer emerging strain has a greater reproduction number is verified numerically. The effect of vaccines on the population is also analyzed and a bound for the herd immunity threshold is calculated. The validity of the work done is verified through numerical simulations by applying the proposed model and strategy to analyze the multi-strains of the COVID-19 virus, in particular, the Delta and the Omicron variants, in the United State.

Mask Use to Curtail Influenza in a Post-COVID-19 World: Modeling Study

Background

Face mask mandates have been instrumental in the reduction of transmission of airborne COVID-19. Thus, the question arises whether comparatively mild measures should be kept in place after the pandemic to reduce other airborne diseases such as influenza.

Objective

In this study, we aim to simulate the quantitative impact of face masks on the rate of influenza illnesses in the United States.

Methods

Using the Centers for Disease Control and Prevention data from 2010 to 2019, we used a series of differential equations to simulate past influenza seasons, assuming that people wore face masks. This was achieved by introducing a variable to account for the efficacy and prevalence of masks and then analyzing its impact on influenza transmission rate in a susceptible-exposed-infected-recovered model fit to the actual past seasons. We then compared influenza rates in this hypothetical scenario with the actual rates over the seasons.

Results

Our results show that several combinations of mask efficacy and prevalence can substantially reduce the burden of seasonal influenza. Across all the years modeled, a mask prevalence of 0.2 (20%) and assumed moderate inward and outward mask efficacy of 0.45 (45%) reduced influenza infections by >90%.

Conclusions

A minority of individuals wearing masks substantially reduced the number of influenza infections across seasons. Considering the efficacy rates of masks and the relatively insignificant monetary cost, we highlight that it may be a viable alternative or complement to influenza vaccinations.

Incentives, lockdown, and testing: from Thucydides’ analysis to the COVID-19 pandemic

In this work, we provide a general mathematical formalism to study the optimal control of an epidemic, such as the COVID-19 pandemic, via incentives to lockdown and testing. In particular, we model the interplay between the government and the population as a principal–agent problem with moral hazard, à la Cvitanić et al. (Finance Stoch 22(1):1–37, 2018), while an epidemic is spreading according to dynamics given by compartmental stochastic SIS or SIR models, as proposed respectively by Gray et al. (SIAM J Appl Math 71(3):876–902, 2011) and Tornatore et al. (Phys A Stat Mech Appl 354(15):111–126, 2005). More precisely, to limit the spread of a virus, the population can decrease the transmission rate of the disease by reducing interactions between individuals. However, this effort—which cannot be perfectly monitored by the government—comes at social and monetary cost for the population. To mitigate this cost, and thus encourage the lockdown of the population, the government can put in place an incentive policy, in the form of a tax or subsidy. In addition, the government may also implement a testing policy in order to know more precisely the spread of the epidemic within the country, and to isolate infected individuals. In terms of technical results, we demonstrate the optimal form of the tax, indexed on the proportion of infected individuals, as well as the optimal effort of the population, namely the transmission rate chosen in response to this tax. The government’s optimisation problems then boils down to solving an Hamilton–Jacobi–Bellman equation. Numerical results confirm that if a tax policy is implemented, the population is encouraged to significantly reduce its interactions. If the government also adjusts its testing policy, less effort is required on the population side, individuals can interact almost as usual, and the epidemic is largely contained by the targeted isolation of positively-tested individuals.

The limit behavior of SEIRS model in spatial grid

In this paper, we study a SEIRS model with Neumann boundary condition for a population distributed in a spatial grid. We first discuss the existence and uniqueness of global positive solution with any given positive initial value. Next, we introduce the basic reproduction number of this model. Then we consider the relation between the system of PDE and the discrete ODE model. Finally, we consider the stochastic model and give two laws of large numbers.

Applying the Spatial Transmission Network to the Forecast of Infectious Diseases Across Multiple Regions

Objective

Timely and accurate forecast of infectious diseases is essential for achieving precise prevention and control. A good forecasting method of infectious diseases should have the advantages of interpretability, feasibility, and forecasting performance. Since previous research had illustrated that the spatial transmission network (STN) showed good interpretability and feasibility, this study further explored its forecasting performance for infectious diseases across multiple regions. Meanwhile, this study also showed whether the STN could overcome the challenges of model rationality and practical needs.

Methods

The construction of the STN framework involved three major steps: the spatial kluster analysis by tree edge removal (SKATER) algorithm, structure learning by dynamic Bayesian network (DBN), and parameter learning by the vector autoregressive moving average (VARMA) model. Then, we evaluated the forecasting performance of STN by comparing its accuracy with that of the mechanism models like susceptible-exposed-infectious-recovered-susceptible (SEIRS) and machine-learning algorithm like long-short-term memory (LSTM). At the same time, we assessed the robustness of forecasting performance of STN in high and low incidence seasons. The influenza-like illness (ILI) data in the Sichuan Province of China from 2010 to 2017 were used as an example for illustration.

Results

The STN model revealed that ILI was likely to spread among multiple cities in Sichuan during the study period. During the whole study period, the forecasting accuracy of the STN (mean absolute percentage error [MAPE] = 31.134) was significantly better than that of the LSTM (MAPE = 41.657) and the SEIRS (MAPE = 62.039). In addition, the forecasting performance of STN was also superior to those of the other two methods in either the high incidence season (MAPE = 24.742) or the low incidence season (MAPE = 26.209), and the superiority was more obvious in the high incidence season.

Conclusion

This study applied the STN to the forecast of infectious diseases across multiple regions. The results illustrated that the STN not only had good accuracy in forecasting performance but also indicated the spreading directions of infectious diseases among multiple regions to a certain extent. Therefore, the STN is a promising candidate to improve the surveillance work.

A Stochastic SEIRS Epidemic Model with Infection Forces and Intervention Strategies

The spread of epidemics has been extensively investigated using susceptible-exposed infectious-recovered-susceptible (SEIRS) models. In this work, we propose a SEIRS pandemic model with infection forces and intervention strategies. The proposed model is characterized by a stochastic differential equation (SDE) framework with arbitrary parameter settings. Based on a Markov semigroup hypothesis, we demonstrate the effect of the proliferation number R 0 S on the SDE solution. On the one hand, when R 0 S < 1, the SDE has an illness-free solution set under gentle additional conditions. This implies that the epidemic can be eliminated with a likelihood of 1. On the other hand, when R 0 S > 1, the SDE has an endemic stationary circulation under mild additional conditions. This prompts the stochastic regeneration of the epidemic. Also, we show that arbitrary fluctuations can reduce the infection outbreak. Hence, valuable procedures can be created to manage and control epidemics.

How Can Hybrid Simulation Support Organizations in Assessing COVID-19 Containment Measures?

Simulation models have always been an aid in epidemiology for understanding the spread of epidemics and evaluating their containment policies. This paper illustrates how hybrid simulation can support companies in assessing COVID-19 containment measures in indoor environments. In particular, a Hybrid Simulation (HS) is presented. The HS model consists of an Agent-Based Simulation (ABS) to simulate the virus contagion model and a Discrete Event Simulation (DES) model to simulate the interactions between flows of people in an indoor environment. Compared with previous works in the field of simulation and COVID-19, this study provides the possibility to model the specific behaviors of individuals moving in time and space and the proposed HS model could be adapted to several epidemiological conditions (just setting different parameters in the agent-based model) and different kinds of facilities. The HS approach has been developed and then successfully tested with a real case study related to a university campus in northern Italy. The case study highlights the potentials of hybrid simulation in assessing the effectiveness of the containment measures adopted during the period under examination in the pandemic context. From a managerial perspective, this study, exploiting the complementarity of the ABM and DES approaches in a HS model, provides a complete and usable tool to support decision-makers in evaluating different contagion containment measures.

Estimation of epidemiological parameters for COVID-19 cases using a stochastic SEIRS epidemic model with vital dynamics

We estimate and analyze the time-dependent parameters: transmission rate, symptomatic recovery rate, immunity rate, infection noise intensities, and the effective reproduction number for the United States COVID-19 cases for the period 01/22/2020-02/25/2021 using an innovative generalized method of moments estimation scheme. We assume the disease-dynamic is described by a stochastic susceptible-exposed-infected-recovered-susceptible (SEIRS) epidemic model, where the infected class is divided into the asymptomatic infected, and symptomatic infectious classes. Stochasticity appears in the model due to fluctuations in the disease's transmission and recovery rates. The disease eradication threshold is derived from the reproduction number. The estimated parameters are used to model the disease outbreak's possible trajectories. Our analysis reveals that current interventions are having positive effects on the transmission and recovery rates. The analysis is demonstrated using the daily United States COVID-19 infection and recovered cases for the period: 01/22/2020-02/25/2021.

Time-dependent probability distribution for number of infection in a stochastic SIS model: case study COVID-19

We derive the time-dependent probability distribution for the number of infected individuals at a given time in a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model. The mean, variance, skewness, and kurtosis of the distribution are obtained as a function of time. We study the effect of noise intensity on the distribution and later derive and analyze the effect of changes in the transmission and recovery rates of the disease. Our analysis reveals that the time-dependent probability density function exists if the basic reproduction number is greater than one. It converges to the Dirac delta function on the long run (entirely concentrated on zero) as the basic reproduction number tends to one from above. The result is applied using published COVID-19 parameters and also applied to analyze the probability distribution of the aggregate number of COVID-19 cases in the United States for the period: January 22, 2020-March 23, 2021. Findings show that the distribution shifts concentration to the right until it concentrates entirely on the carrying infection capacity as the infection growth rate increases or the recovery rate reduces. The disease eradication and disease persistence thresholds are calculated.

A stochastic epidemic model with infectivity in incubation period and homestead-isolation on the susceptible

A stochastic epidemic model with infectivity rate in incubation period and homestead-isolation on the susceptible is developed with the aim of revealing the effect of stochastic white noise on the long time behavior. A good understanding of extinction and strong persistence in the mean of the disease is obtained. Also, we derive sufficient criteria for the existence of a unique ergodic stationary distribution of the model. Our theoretical results show that the suitably large noise can make the disease extinct while the relatively small noise is advantageous for persistence of the disease and stationary distribution.

Identifiability analysis for stochastic differential equation models in systems biology

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

A network model of Italy shows that intermittent regional strategies can alleviate the COVID-19 epidemic

The COVID-19 epidemic hit Italy particularly hard, yielding the implementation of strict national lockdown rules. Previous modelling studies at the national level overlooked the fact that Italy is divided into administrative regions which can independently oversee their own share of the Italian National Health Service. Here, we show that heterogeneity between regions is essential to understand the spread of the epidemic and to design effective strategies to control the disease. We model Italy as a network of regions and parameterize the model of each region on real data spanning over two months from the initial outbreak. We confirm the effectiveness at the regional level of the national lockdown strategy and propose coordinated regional interventions to prevent future national lockdowns, while avoiding saturation of the regional health systems and mitigating impact on costs. Our study and methodology can be easily extended to other levels of granularity to support policy- and decision-makers.

Phenomenological dynamics of COVID-19 pandemic: Meta-analysis for adjustment parameters

We present a phenomenological procedure of dealing with the COVID-19 (coronavirus disease 2019) data provided by government health agencies of 11 different countries. Usually, the exact or approximate solutions of susceptible-infected-recovered (or other) model(s) are obtained fitting the data by adjusting the time-independent parameters that are included in those models. Instead of that, in this work, we introduce dynamical parameters whose time-dependence may be phenomenologically obtained by adequately extrapolating a chosen subset of the daily provided data. This phenomenological approach works extremely well to properly adjust the number of infected (and removed) individuals in time for the countries we consider. Besides, it can handle the sub-epidemic events that some countries may experience. In this way, we obtain the evolution of the pandemic without using any a priori model based on differential equations.

Unravelling the myths of R 0 in controlling the dynamics of COVID-19 outbreak: A modelling perspective

COVID-19 is an emerging and rapidly evolving pandemic around the world, which causes severe acute respiratory syndrome and results in substantial morbidity and mortality. To examine the transmission dynamics of COVID-19, we investigate the spread of this pandemic using Malaysia as a case study and scrutinise its interactions with some exogenous factors such as limited medical resources and false detection problems. To do this, we employ a simple epidemiological model and analyse this system using modelling and dynamical systems techniques. We discover some contrasting findings with respect to the observations of basic reproduction number: while it is observed that R ₀ seems to provide a good description of transmission dynamics in simple outbreak scenarios, this quantity might mislead the assessment on the severity of pandemic when certain complexities such as limited medical resources and false detection problems are incorporated into the model. In particular, we observe the possibility of a COVID-19 outbreak through bistable behaviour, even when the basic reproduction number is less than unity. Based on these findings, we caution policy makers not to make their decisions solely based on the guidance of the basic reproduction number only, which clearly could cause trouble.

Locally Informed Simulation to Predict Hospital Capacity Needs During the COVID-19 Pandemic

BACKGROUND

The coronavirus disease 2019 (COVID-19) pandemic challenges hospital leaders to make time-sensitive, critical decisions about clinical operations and resource allocations.

OBJECTIVE

To estimate the timing of surges in clinical demand and the best- and worst-case scenarios of local COVID-19-induced strain on hospital capacity, and thus inform clinical operations and staffing demands and identify when hospital capacity would be saturated.

DESIGN

Monte Carlo simulation instantiation of a susceptible, infected, removed (SIR) model with a 1-day cycle.

SETTING

3 hospitals in an academic health system.

PATIENTS

All people living in the greater Philadelphia region.

MEASUREMENTS

The COVID-19 Hospital Impact Model (CHIME) (http://penn-chime.phl.io) SIR model was used to estimate the time from 23 March 2020 until hospital capacity would probably be exceeded, and the intensity of the surge, including for intensive care unit (ICU) beds and ventilators.

RESULTS

Using patients with COVID-19 alone, CHIME estimated that it would be 31 to 53 days before demand exceeds existing hospital capacity. In best- and worst-case scenarios of surges in the number of patients with COVID-19, the needed total capacity for hospital beds would reach 3131 to 12 650 across the 3 hospitals, including 338 to 1608 ICU beds and 118 to 599 ventilators.

LIMITATIONS

Model parameters were taken directly or derived from published data across heterogeneous populations and practice environments and from the health system's historical data. CHIME does not incorporate more transition states to model infection severity, social networks to model transmission dynamics, or geographic information to account for spatial patterns of human interaction.

CONCLUSION

Publicly available and designed for hospital operations leaders, this modeling tool can inform preparations for capacity strain during the early days of a pandemic.

PRIMARY FUNDING SOURCE

University of Pennsylvania Health System and the Palliative and Advanced Illness Research Center.

Prediction of COVID-19 Outbreak in China and Optimal Return Date for University Students Based on Propagation Dynamics

On 12 December 2019, a novel coronavirus disease, named COVID-19, began to spread around the world from Wuhan, China. It is useful and urgent to consider the future trend of this outbreak. We establish the 4+1 penta-group model to predict the development of the COVID-19 outbreak. In this model, we use the collected data to calibrate the parameters, and let the recovery rate and mortality change according to the actual situation. Furthermore, we propose the BAT model, which is composed of three parts: simulation of the return rush (Back), analytic hierarchy process (AHP) method, and technique for order preference by similarity to an ideal solution (TOPSIS) method, to figure out the best return date for university students. We also discuss the impacts of some factors that may occur in the future, such as secondary infection, emergence of effective drugs, and population flow from Korea to China.

Qualitative analysis of a stochastic SEITR epidemic model with multiple stages of infection and treatment

We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external fluctuations in the transmission, treatment and recovery rates. We assume external fluctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By defining RT,n and RT,n as the basic deterministic and stochastic reproduction numbers, respectively, in stage n of infection and treatment, we show mathematically that as the intensity of the noise in the transmission, treatment and recovery rates increases, the number of secondary cases of infection increases. The global stability of the disease-free and endemic equilibrium for the deterministic and stochastic SEITR models is also presented. The work presented is demonstrated using parameter values relevant to the transmission dynamics of Influenza in the United States from October 1, 2018 through May 4, 2019 influenza seasons.

Closed-form probability distribution of number of infections at a given time in a stochastic SIS epidemic model

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to a generalized Laguerre differential equation. The properties of the distribution, together with the effect of noise intensity, are analyzed. The distribution is demonstrated using parameter values relevant to the transmission dynamics of influenza in the United States.