Effects of latency and age structure on the dynamics and containment of COVID-19

A model-based strategy for the COVID-19 vaccine roll-out in the Philippines

COVID-19 has affected millions of people worldwide, causing illness and death, and disrupting daily life while imposing a significant social and economic burden. Vaccination is an important control measure that significantly reduces mortality if properly and efficiently distributed. In this work, an age-structured model of COVID-19 transmission, incorporating an unreported infectious compartment, is developed. Three age groups are considered: young (0-19 years), adult (20-64 years), and elderly (65+ years). The transmission rate and reporting rate are determined for each group by utilizing the number of COVID-19 cases in the National Capital Region in the Philippines. Optimal control theory is employed to identify the best vaccine allocation to different age groups. Further, three different vaccination periods are considered to reflect phases of vaccination priority groups: the first, second, and third account for the inoculation of the elderly, adult and elderly, and all three age groups, respectively. This study could guide in making informed decisions in mitigating a population-structured disease transmission under limited resources.

Evaluations of heterogeneous epidemic models with exponential and non-exponential distributions for latent period: the Case of COVID-19

Most of heterogeneous epidemic models assume exponentially distributed sojourn times in infectious states, which may not be practical in reality and could affect the dynamics of the epidemic. This paper investigates the potential discrepancies between exponential and non-exponential distribution models in analyzing the transmission patterns of infectious diseases and evaluating control measures. Two SEIHR models with multiple subgroups based on different assumptions for latency are established: Model Ⅰ assumes an exponential distribution of latency, while Model Ⅱ assumes a gamma distribution. To overcome the challenges associated with the high dimensionality of GDM, we derive the basic reproduction number ($ R_{0} $) of the model theoretically, and apply numerical simulations to evaluate the effect of different interventions on EDM and GDM. Our results show that considering a more realistic gamma distribution of latency can change the peak numbers of infected and the timescales of an epidemic, and GDM may underestimate the infection eradication time and overestimate the peak value compared to EDM. Additionally, the two models can produce inconsistent predictions in estimating the time to reach the peak. Our study contributes to a more accurate understanding of disease transmission patterns, which is crucial for effective disease control and prevention.

Global stability of latency-age/stage-structured epidemic models with differential infectivity

In this paper, we first formulate a system of ODEs-PDE to model diseases with latency-age and differential infectivity. Then, based on the ways how latent individuals leave the latent stage, one ODE and two DDE models are derived. We only focus on the global stability of the models. All the models have some similarities in the existence of equilibria. Each model has a threshold dynamics for global stability, which is completely characterized by the basic reproduction number. The approach is the Lyapunov direct method. We propose an idea on constructing Lyapunov functionals for the two DDE and the original ODEs-PDE models. During verifying the negative (semi-)definiteness of derivatives of the Lyapunov functionals along solutions, a novel positive definite function and a new inequality are used. The idea here is also helpful in applying the Lyapunov direct method to prove the global stability of some epidemic models with age structure or delays.

Modified susceptible-exposed-infectious-recovered model for assessing the effectiveness of non-pharmaceutical interventions during the COVID-19 pandemic in Seoul

Susceptible-exposed-infectious-recovered (SEIR) models were applied to assess the effectiveness of non-pharmaceutical interventions (NPIs) and to study the dynamic behavior of the COVID-19 pandemic. Recently, SEIR models have evolved to address the change of human mobility by some NPIs for predicting the new confirmed cases. However, the models have serious limitations when applied to Seoul. Seoul has two representative quarantine policies, i.e. social distancing and the ban on gatherings. Effects of the two policies need to be reflected in different functional forms in the model because changes in human mobility do not fully reflect the ban on gatherings. Thus we propose a modified SEIR model to assess the effectiveness of social distancing, ban on gatherings and vaccination strategies. The application of the modified SEIR model was illustrated by comparing the model output with real data.

Evaluations of COVID-19 epidemic models with multiple susceptible compartments using exponential and non-exponential distribution for disease stages

Mathematical models have wide applications in studying COVID-19 epidemic transmission dynamics, however, most mathematical models do not take into account the heterogeneity of susceptible populations and the non-exponential distribution infectious period. This paper attempts to investigate whether non-exponentially distributed infectious period can better characterize the transmission process in heterogeneous susceptible populations and how it impacts the control strategies. For this purpose, we establish two COVID-19 epidemic models with heterogeneous susceptible populations based on different assumptions for infectious period: the first one is an exponential distribution model (EDM), and the other one is a gamma distribution model (GDM); explicit formula of peak time of the EDM is presented via our analytical approach. By data fitting with the COVID-19 (Omicron) epidemic in Spain and Norway, it seems that Spain is more suitable for EDM while Norway is more suitable for GDM. Finally, we use EDM and GDM to evaluate the impaction of control strategies such as reduction of transmission rates, and increase of primary course rate (PCR) and booster dose rate (BDR).

Impact of age structure and vaccine prioritization on COVID-19 in West Africa

The ongoing COVID-19 pandemic has been a major global health challenge since its emergence in 2019. Contrary to early predictions that sub-Saharan Africa (SSA) would bear a disproportionate share of the burden of COVID-19 due to the region's vulnerability to other infectious diseases, weak healthcare systems, and socioeconomic conditions, the pandemic's effects in SSA have been very mild in comparison to other regions. Interestingly, the number of cases, hospitalizations, and disease-induced deaths in SSA remain low, despite the loose implementation of non-pharmaceutical interventions (NPIs) and the low availability and administration of vaccines. Possible explanations for this low burden include epidemiological disparities, under-reporting (due to limited testing), climatic factors, population structure, and government policy initiatives. In this study, we formulate a model framework consisting of a basic model (in which only susceptible individuals are vaccinated), a vaccine-structured model, and a hybrid vaccine-age-structured model to assess the dynamics of COVID-19 in West Africa (WA). The framework is trained with a portion of the confirmed daily COVID-19 case data for 16 West African countries, validated with the remaining portion of the data, and used to (i) assess the effect of age structure on the incidence of COVID-19 in WA, (ii) evaluate the impact of vaccination and vaccine prioritization based on age brackets on the burden of COVID-19 in the sub-region, and (iii) explore plausible reasons for the low burden of COVID-19 in WA compared to other parts of the world. Calibration of the model parameters and global sensitivity analysis show that asymptomatic youths are the primary drivers of the pandemic in WA. Also, the basic and control reproduction numbers of the hybrid vaccine-age-structured model are smaller than those of the other two models indicating that the disease burden is overestimated in the models which do not account for age-structure. This result is confirmed through the vaccine-derived herd immunity thresholds. In particular, a comprehensive analysis of the basic (vaccine-structured) model reveals that if 84%(73%) of the West African populace is fully immunized with the vaccines authorized for use in WA, vaccine-derived herd immunity can be achieved. This herd immunity threshold is lower (68%) for the hybrid model. Also, all three thresholds are lower (60% for the basic model, 51% for the vaccine-structured model, and 48% for the hybrid model) if vaccines of higher efficacies (e.g., the Pfizer or Moderna vaccine) are prioritized, and higher if vaccines of lower efficacy are prioritized. Simulations of the models show that controlling the COVID-19 pandemic in WA (by reducing transmission) requires a proactive approach, including prioritizing vaccination of more youths or vaccination of more youths and elderly simultaneously. Moreover, complementing vaccination with a higher level of mask compliance will improve the prospects of containing the pandemic. Additionally, simulations of the model predict another COVID-19 wave (with a smaller peak size compared to the Omicron wave) by mid-July 2022. Furthermore, the emergence of a more transmissible variant or easing the existing measures that are effective in reducing transmission will result in more devastating COVID-19 waves in the future. To conclude, accounting for age-structure is important in understanding why the burden of COVID-19 has been low in WA and sustaining the current vaccination level, complemented with the WHO recommended NPIs is critical in curbing the spread of the disease in WA.

Preventive control strategy on second wave of Covid-19 pandemic model incorporating lock-down effect

This study presents an optimal control strategy through a mathematical model of the Covid-19 outbreak without lock-down. The pandemic model analyses the lock-down effect without control strategy based on the current scenario of second wave data to control the rapid spread of the virus. The pandemic model has been discussed with respect to the basic reproduction number and stability analysis of disease-free and endemic equilibrium. A new optimal control problem with treatment is framed to minimize the vulnerable situation of the second wave. This system is applied to study the effects of vaccines and treatment controls. Numerical solutions and the graphical presentation of the results predict the fate of India’s second wave situation on account of the control strategy. Lastly, a comparative study with control and without control has been analysed for the exposed phase, infective phase, and recovery phase to understand the effectiveness of the controls. This model is used to estimate the total number of infected and active cases, deaths, and recoveries in order to control the disease using this system and studying the effects of vaccines and treatment controls.

Prediction of COVID-19 Data Using Hybrid Modeling Approaches

A major emphasis is the dissemination of COVID-19 across the country's many regions and provinces. Using the present COVID-19 pandemic as a guide, the researchers suggest a hybrid model architecture for analyzing and optimizing COVID-19 data during the complete country. The analysis of COVID-19's exploration and death rate uses an ARIMA model with susceptible-infectious-removed and susceptible-exposed-infectious-removed (SEIR) models. The logistic model's failure to forecast the number of confirmed diagnoses and the snags of the SEIR model's too many tuning parameters are both addressed by a hybrid model method. Logistic regression (LR), Autoregressive Integrated Moving Average Model (ARIMA), support vector regression (SVR), multilayer perceptron (MLP), Recurrent Neural Networks (RNN), Gate Recurrent Unit (GRU), and long short-term memory (LSTM) are utilized for the same purpose. Root mean square error, mean absolute error, and mean absolute percentage error are used to show these models. New COVID-19 cases, the number of quarantines, mortality rates, and the deployment of public self-protection measures to reduce the epidemic are all outlined in the study's findings. Government officials can use the findings to guide future illness prevention and control choices.

Designing social distancing policies for the COVID-19 pandemic: A probabilistic model predictive control approach

The effective control of the COVID-19 pandemic is one the most challenging issues of recent years. The design of optimal control policies is challenging due to a variety of social, political, economical and epidemiological factors. Here, based on epidemiological data reported in recent studies for the Italian region of Lombardy, which experienced one of the largest and most devastating outbreaks in Europe during the first wave of the pandemic, we present a probabilistic model predictive control (PMPC) approach for the systematic study of what if scenarios of social distancing in a retrospective analysis for the first wave of the pandemic in Lombardy. The performance of the proposed PMPC was assessed based on simulations of a compartmental model that was developed to quantify the uncertainty in the level of the asymptomatic cases in the population, and the synergistic effect of social distancing during various activities, and public awareness campaign prompting people to adopt cautious behaviors to reduce the risk of disease transmission. The PMPC takes into account the social mixing effect, i.e. the effect of the various activities in the potential transmission of the disease. The proposed approach demonstrates the utility of a PMPC approach in addressing COVID-19 transmission and implementing public relaxation policies.

The influence of gender on COVID-19 infections and mortality in Germany: Insights from age- and gender-specific modeling of contact rates, infections, and deaths in the early phase of the pandemic

Recent research points towards age- and gender-specific transmission of COVID-19 infections and their outcomes. The effect of gender, however, has been overlooked in past modelling approaches of COVID-19 infections. The aim of our study is to explore how gender-specific contact behavior affects gender-specific COVID-19 infections and deaths. We consider a compartment model to establish short-term forecasts of the COVID-19 epidemic over a time period of 75 days. Compartments are subdivided into different age groups and genders, and estimated contact patterns, based on previous studies, are incorporated to account for age- and gender-specific social behaviour. The model is fitted to real data and used for assessing the effect of hypothetical contact scenarios all starting at a daily level of 10 new infections per million population. On day 75 after the end of the lockdown, infection rates are highest among the young and working-age, but they also have increased among the old. Sex ratios reveal higher infection risks among women than men at working ages; the opposite holds true at old age. Death rates in all age groups are twice as high for men as for women. Small changes in contact rates at working and young ages have a considerable effect on infections and mortality at old age, with elderly men being always at higher risk of infection and mortality. Our results underline the high importance of the non-pharmaceutical mitigation measures (NPMM) in low-infection phases of the pandemic to prevent that an increase in contact rates leads to higher mortality among the elderly, even if easing measures take place among the young. At young and middle ages, women's contribution to increasing infections is higher due to their higher number of contacts. Gender differences in contact rates may be one pathway that contributes to the spread of the disease and results in gender-specific infection rates and their mortality outcome. To further explore possible pathways, more data on contact behavior and COVID-19 transmission is needed, which includes gender- and socio-demographic information.

COVID-19 transmission risk factors

We analyze risk factors correlated with the initial transmission growth rate of the recent COVID-19 pandemic in different countries. The number of cases follows in its early stages an almost exponential expansion; we chose as a starting point in each country the first day di with 30 cases and we fitted for 12 days, capturing thus the early exponential growth. We looked then for linear correlations of the exponents α with other variables, for a sample of 126 countries. We find a positive correlation, i.e. faster spread of COVID-19, with high confidence level with the following variables, with respective p-value: low Temperature (4⋅10-7), high ratio of old vs. working-age people (3⋅10-6), life expectancy (8⋅10-6), number of international tourists (1⋅10-5), earlier epidemic starting date di (2⋅10-5), high level of physical contact in greeting habits (6⋅10-5), lung cancer prevalence (6⋅10-5), obesity in males (1⋅10-4), share of population in urban areas (2⋅10-4), cancer prevalence (3⋅10-4), alcohol consumption (0.0019), daily smoking prevalence (0.0036), and UV index (0.004, 73 countries). We also find a correlation with low Vitamin D serum levels (0.002-0.006), but on a smaller sample, ∼50 countries, to be confirmed on a larger sample. There is highly significant correlation also with blood types: positive correlation with types RH- (3⋅10-5) and A+ (3⋅10-3), negative correlation with B+ (2⋅10-4). We also find positive correlation with moderate confidence level (p-value of 0.02∼0.03) with: CO₂/SO emissions, type-1 diabetes in children, low vaccination coverage for Tuberculosis (BCG). Several of the above variables are correlated with each other, and so they are likely to have common interpretations. We thus performed a Principal Component Analysis, to find the significant independent linear combinations of such variables. The variables with loadings of at least 0.3 on the significant PCA are: greeting habits, urbanization, epidemic starting date, number of international tourists, temperature, lung cancer, smoking, and obesity in males. We also analyzed the possible existence of a bias: countries with low GDP-per capita might have less intense testing, and we discuss correlation with the above variables.

COVID-19 transmission risk factors

We analyze risk factors correlated with the initial transmission growth rate of the recent COVID-19 pandemic in different countries. The number of cases follows in its early stages an almost exponential expansion; we chose as a starting point in each country the first day d i with 30 cases and we fitted for 12 days, capturing thus the early exponential growth. We looked then for linear correlations of the exponents α with other variables, for a sample of 126 countries. We find a positive correlation, i.e. faster spread of COVID-19, with high confidence level with the following variables, with respective p -value: low Temperature (4 ⋅ 10 - 7 ), high ratio of old vs. working-age people (3 ⋅ 10 - 6 ), life expectancy (8 ⋅ 10 - 6 ), number of international tourists (1 ⋅ 10 - 5 ), earlier epidemic starting date d i (2 ⋅ 10 - 5 ), high level of physical contact in greeting habits (6 ⋅ 10 - 5 ), lung cancer prevalence (6 ⋅ 10 - 5 ), obesity in males (1 ⋅ 10 - 4 ), share of population in urban areas (2 ⋅ 10 - 4 ), cancer prevalence (3 ⋅ 10 - 4 ), alcohol consumption (0.0019 ), daily smoking prevalence (0.0036 ), and UV index (0.004 , 73 countries). We also find a correlation with low Vitamin D serum levels (0.002 - 0.006 ), but on a smaller sample, ∼ 50 countries, to be confirmed on a larger sample. There is highly significant correlation also with blood types: positive correlation with types RH- (3 ⋅ 10 - 5 ) and A+ (3 ⋅ 10 - 3 ), negative correlation with B+ (2 ⋅ 10 - 4 ). We also find positive correlation with moderate confidence level (p -value of 0.02 ∼ 0.03 ) with: CO2/SO emissions, type-1 diabetes in children, low vaccination coverage for Tuberculosis (BCG). Several of the above variables are correlated with each other, and so they are likely to have common interpretations. We thus performed a Principal Component Analysis, to find the significant independent linear combinations of such variables. The variables with loadings of at least 0.3 on the significant PCA are: greeting habits, urbanization, epidemic starting date, number of international tourists, temperature, lung cancer, smoking, and obesity in males. We also analyzed the possible existence of a bias: countries with low GDP-per capita might have less intense testing, and we discuss correlation with the above variables.

Regional opening strategies with commuter testing and containment of new SARS-CoV-2 variants in Germany

BACKGROUND

Despite the vaccination process in Germany, a large share of the population is still susceptible to SARS-CoV-2. In addition, we face the spread of novel variants. Until we overcome the pandemic, reasonable mitigation and opening strategies are crucial to balance public health and economic interests.

METHODS

We model the spread of SARS-CoV-2 over the German counties by a graph-SIR-type, metapopulation model with particular focus on commuter testing. We account for political interventions by varying contact reduction values in private and public locations such as homes, schools, workplaces, and other. We consider different levels of lockdown strictness, commuter testing strategies, or the delay of intervention implementation. We conduct numerical simulations to assess the effectiveness of the different intervention strategies after one month. The virus dynamics in the regions (German counties) are initialized randomly with incidences between 75 and 150 weekly new cases per 100,000 inhabitants (red zones) or below (green zones) and consider 25 different initial scenarios of randomly distributed red zones (between 2 and 20% of all counties). To account for uncertainty, we consider an ensemble set of 500 Monte Carlo runs for each scenario.

RESULTS

We find that the strength of the lockdown in regions with out of control virus dynamics is most important to avoid the spread into neighboring regions. With very strict lockdowns in red zones, commuter testing rates of twice a week can substantially contribute to the safety of adjacent regions. In contrast, the negative effect of less strict interventions can be overcome by high commuter testing rates. A further key contributor is the potential delay of the intervention implementation. In order to keep the spread of the virus under control, strict regional lockdowns with minimum delay and commuter testing of at least twice a week are advisable. If less strict interventions are in favor, substantially increased testing rates are needed to avoid overall higher infection dynamics.

CONCLUSIONS

Our results indicate that local containment of outbreaks and maintenance of low overall incidence is possible even in densely populated and highly connected regions such as Germany or Western Europe. While we demonstrate this on data from Germany, similar patterns of mobility likely exist in many countries and our results are, hence, generalizable to a certain extent.

Mathematical modelling of earlier stages of COVID-19 transmission dynamics in Ghana

In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of the world, the impact on the local health service is still significant. Compartmental models are a useful framework for investigating transmission of diseases in societies. To understand how the infection will spread and how to limit the outbreak. We have developed a modified SEIR compartmental model with nine compartments (CoVCom9) to describe the dynamics of SARS-CoV-2 transmission in Ghana. We have carried out a detailed mathematical analysis of the CoVCom9, including the derivation of the basic reproduction number, R 0 . In particular, we have shown that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 via a candidate Lyapunov function. Using the SARS-CoV-2 reported data for confirmed-positive cases and deaths from March 13 to August 10, 2020, we have parametrised the CoVCom9 model. The results of this fit show good agreement with data. We used Latin hypercube sampling-rank correlation coefficient (LHS-PRCC) to investigate the uncertainty and sensitivity of R 0 since the results derived are significant in controlling the spread of SARS-CoV-2. We estimate that over this five month period, the basic reproduction number is given by R 0 = 3 . 110 , with the 95% confidence interval being 2 . 042 ≤ R 0 ≤ 3 . 240 , and the mean value being R 0 = 2 . 623 . Of the 32 parameters in the model, we find that just six have a significant influence on R 0 , these include the rate of testing, where an increasing testing rate contributes to the reduction of R 0 .

A new threshold reveals the uncertainty about the effect of school opening on diffusion of Covid-19

Studies on the effects of school openings or closures during the Covid-19 pandemic seem to reach contrasting conclusions even in similar contexts. We aim at clarifying this controversy. A mathematical analysis of compartmental models with subpopulations has been conducted, starting from the SIR model, and progressively adding features modeling outbreaks or upsurge of variants, lockdowns, and vaccinations. We find that in all cases, the in-school transmission rates only affect the overall course of the pandemic above a certain context dependent threshold. We provide rigorous proofs and computations of the thresdhold through linearization. We then confirm our theoretical findings through simulations and the review of data-driven studies that exhibit an often unnoticed phase transition. Specific implications are: awareness about the threshold could inform choice of data collection, analysis and release, such as in-school transmission rates, and clarify the reason for divergent conclusions in similar studies; schools may remain open at any stage of the Covid-19 pandemic, including variants upsurge, given suitable containment rules; these rules would be extremely strict and hardly sustainable if only adults are vaccinated, making a compelling argument for vaccinating children whenever possible.

Safety-Critical Control of Compartmental Epidemiological Models With Measurement Delays

We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and human interventions (such as quarantining or social distancing) as control input. We consider a generalized compartmental model that represents the form of the most popular epidemiological models and we design safety-critical controllers that formally guarantee safe evolution with respect to keeping certain populations of interest under prescribed safe limits. Furthermore, we discuss how measurement delays originated from incubation period and testing delays affect safety and how delays can be compensated via predictor feedback. We demonstrate our results by synthesizing active intervention policies that bound the number of infections, hospitalizations and deaths for epidemiological models capturing the spread of COVID-19 in the USA.

Exploring the Spatiotemporal Characteristics of COVID-19 Infections among Healthcare Workers: A Multi-Scale Perspective

The outbreak of COVID-19 has constantly exposed health care workers (HCWs) around the world to a high risk of infection. To more accurately discover the infection differences among high-risk occupations and institutions, Hubei Province was taken as an example to explore the spatiotemporal characteristics of HCWs at different scales by employing the chi-square test and fitting distribution. The results indicate (1) the units around the epicenter of the epidemic present lognormal distribution, and the periphery is Poisson distribution. There is a clear dividing line between lognormal and Poisson distribution in terms of the number of HCWs infections. (2) The infection rates of different types of HCWs at multiple geospatial scales are significantly different, caused by the spatial heterogeneity of the number of HCWs. (3) With the increase of HCWs infection rate, the infection difference among various HCWs also gradually increases and the infection difference becomes more evident on a larger scale. The analysis of the multi-scale infection rate and statistical distribution characteristics of HCWs can help government departments rationally allocate the number of HCWs and personal protective equipment to achieve distribution on demand, thereby reducing the mental and physical pressure and infection rate of HCWs.

Dynamics of partially mitigated multi-phasic epidemics at low susceptible depletion: phases of COVID-19 control in Italy as case study

To mitigate the harmful effects of the COVID-19 pandemic, world countries have resorted - though with different timing and intensities - to a range of interventions. These interventions and their relaxation have shaped the epidemic into a multi-phase form, namely an early invasion phase often followed by a lockdown phase, whose unlocking triggered a second epidemic wave, and so on. In this article, we provide a kinematic description of an epidemic whose time course is subdivided by mitigation interventions into a sequence of phases, on the assumption that interventions are effective enough to prevent the susceptible proportion to largely depart from 100% (or from any other relevant level). By applying this hypothesis to a general SIR epidemic model with age-since-infection and piece-wise constant contact and recovery rates, we supply a unified treatment of this multi-phase epidemic showing how the different phases unfold over time. Subsequently, by exploiting a wide class of infectiousness and recovery kernels allowing reducibility (either to ordinary or delayed differential equations), we investigate in depth a low-dimensional case allowing a non-trivial full analytical treatment also of the transient dynamics connecting the different phases of the epidemic. Finally, we illustrate our theoretical results by a fit to the overall Italian COVID-19 epidemic since March 2020 till February 2021 i.e., before the mass vaccination campaign. This show the abilities of the proposed model in effectively describing the entire course of an observed multi-phasic epidemic with a minimal set of data and parameters, and in providing useful insight on a number of aspects including e.g., the inertial phenomena surrounding the switch between different phases.

Predicting and forecasting the impact of local outbreaks of COVID-19: use of SEIR-D quantitative epidemiological modelling for healthcare demand and capacity

BACKGROUND

The world is experiencing local/regional hotspots and spikes in the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which causes COVID-19 disease. We aimed to formulate an applicable epidemiological model to accurately predict and forecast the impact of local outbreaks of COVID-19 to guide the local healthcare demand and capacity, policy-making and public health decisions.

METHODS

The model utilized the aggregated daily COVID-19 situation reports (including counts of daily admissions, discharges and bed occupancy) from the local National Health Service (NHS) hospitals and COVID-19-related weekly deaths in hospitals and other settings in Sussex (population 1.7 million), Southeast England. These data sets corresponded to the first wave of COVID-19 infections from 24 March to 15 June 2020. A novel epidemiological predictive and forecasting model was then derived based on the local/regional surveillance data. Through a rigorous inverse parameter inference approach, the model parameters were estimated by fitting the model to the data in an optimal sense and then subsequent validation.

RESULTS

The inferred parameters were physically reasonable and matched up to the widely used parameter values derived from the national data sets by Biggerstaff M, Cowling BJ, Cucunubá ZM et al. (Early insights from statistical and mathematical modeling of key epidemiologic parameters of COVID-19, Emerging infectious diseases. 2020;26(11)). We validate the predictive power of our model by using a subset of the available data and comparing the model predictions for the next 10, 20 and 30 days. The model exhibits a high accuracy in the prediction, even when using only as few as 20 data points for the fitting.

CONCLUSIONS

We have demonstrated that by using local/regional data, our predictive and forecasting model can be utilized to guide the local healthcare demand and capacity, policy-making and public health decisions to mitigate the impact of COVID-19 on the local population. Understanding how future COVID-19 spikes/waves could possibly affect the regional populations empowers us to ensure the timely commissioning and organization of services. The flexibility of timings in the model, in combination with other early-warning systems, produces a time frame for these services to prepare and isolate capacity for likely and potential demand within regional hospitals. The model also allows local authorities to plan potential mortuary capacity and understand the burden on crematoria and burial services. The model algorithms have been integrated into a web-based multi-institutional toolkit, which can be used by NHS hospitals, local authorities and public health departments in other regions of the UK and elsewhere. The parameters, which are locally informed, form the basis of predicting and forecasting exercises accounting for different scenarios and impacts of COVID-19 transmission.

A Study of the Correlation between the Dates of the First Covid Case and the First Covid Death of 25 Selected Countries to know the Virulence of the Covid-19 in Different Tropical Conditions

Background

Since December 2019 the highly contagious COVID-19 virus has been spreading worldwide with a rapid spike in the number of deaths. The WHO declared COVID-19 to be a pandemic in March 2020. As of June 2020 it has been 7 months since the first case of COVID-19 was reported in Wuhan, China. So far, COVID-19 has affected more than 24 million people in 215 countries/territories, has caused more than 0.8 million deaths and spread unpredictably quickly among people worldwide. The infection rate in many nations continues to spike. After restraint of the initial outbreak failed, authorities turned to implementing new policies designed to slow the contagion of the virus and the spread of COVID-19 to a manageable rate. This paper presents a systematic analysis to examine in the 25 most affected countries the association between the dates of first death and the first case of the virus to analyse the virulence and also to examine the association between the first case and the virus spread.

Methodology

Data from the WHO website were used. After filtering the data, we calculated the number of days between the first reported case in China and the first reported case in each of the countries, NDFC. Another variable, NDFD, the number of days between the first reported case and first reported case of each country, was also calculated. Then we established the correlation between NDFC and NDFD. Tables are used to show the statistics and charts in order to make the findings clearer.

Results

The date of the first death of each country is not dependant on the first case. When NDFC is high, the variable NDFD is homogeneously low. When the variable NDFC is low, the variable NDFD is heterogeneous. The virus could have been mutating and became more virulent during March. The countries with the highest number of deaths are not the most affected countries when analysing the death ratio of cases and population.

Conclusions

COVID-19 has spread unpredictably quickly among people worldwide. In this critical situation, this paper presents a systematic analysis about the infected cases of COVID-19, deaths and association between first case and first death in each country. In order to obtain a true picture it is necessary to analyse the raw date in different dimensions, and at the end of the paper we will show a clear picture about which countries have controlled the virus very efficiently and which countries have been most affected by it to date.

Inter-provincial disparity of COVID-19 transmission and control in Nepal

Despite the global efforts to mitigate the ongoing COVID-19 pandemic, the disease transmission and the effective controls still remain uncertain as the outcome of the epidemic varies from place to place. In this regard, the province-wise data from Nepal provides a unique opportunity to study the effective control strategies. This is because (a) some provinces of Nepal share an open-border with India, resulting in a significantly high inflow of COVID-19 cases from India; (b) despite the inflow of a considerable number of cases, the local spread was quite controlled until mid-June of 2020, presumably due to control policies implemented; and (c) the relaxation of policies caused a rapid surge of the COVID-19 cases, providing a multi-phasic trend of disease dynamics. In this study, we used this unique data set to explore the inter-provincial disparities of the important indicators, such as epidemic trend, epidemic growth rate, and reproduction numbers. Furthermore, we extended our analysis to identify prevention and control policies that are effective in altering these indicators. Our analysis identified a noticeable inter-province variation in the epidemic trend (3 per day to 104 per day linear increase during third surge period), the median daily growth rate (1 to 4% per day exponential growth), the basic reproduction number (0.71 to 1.21), and the effective reproduction number (maximum values ranging from 1.20 to 2.86). Importantly, results from our modeling show that the type and number of control strategies that are effective in altering the indicators vary among provinces, underscoring the need for province-focused strategies along with the national-level strategy in order to ensure the control of a local spread.

Epidemiological model for the inhomogeneous spatial spreading of COVID-19 and other diseases

We suggest a novel mathematical framework for the in-homogeneous spatial spreading of an infectious disease in human population, with particular attention to COVID-19. Common epidemiological models, e.g., the well-known susceptible-exposed-infectious-recovered (SEIR) model, implicitly assume uniform (random) encounters between the infectious and susceptible sub-populations, resulting in homogeneous spatial distributions. However, in human population, especially under different levels of mobility restrictions, this assumption is likely to fail. Splitting the geographic region under study into areal nodes, and assuming infection kinetics within nodes and between nearest-neighbor nodes, we arrive into a continuous, "reaction-diffusion", spatial model. To account for COVID-19, the model includes five different sub-populations, in which the infectious sub-population is split into pre-symptomatic and symptomatic. Our model accounts for the spreading evolution of infectious population domains from initial epicenters, leading to different regimes of sub-exponential (e.g., power-law) growth. Importantly, we also account for the variable geographic density of the population, that can strongly enhance or suppress infection spreading. For instance, we show how weakly infected regions surrounding a densely populated area can cause rapid migration of the infection towards the populated area. Predicted infection "heat-maps" show remarkable similarity to publicly available heat-maps, e.g., from South Carolina. We further demonstrate how localized lockdown/quarantine conditions can slow down the spreading of disease from epicenters. Application of our model in different countries can provide a useful predictive tool for the authorities, in particular, for planning strong lockdown measures in localized areas-such as those underway in a few countries.

A metapopulation network model for the spreading of SARS-CoV-2: Case study for Ireland

We present preliminary results on an all-Ireland network modelling approach to simulate the spreading the Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2), commonly known as the coronavirus. In the model, nodes correspond to locations or communities that are connected by links indicating travel and commuting between different locations. While this proposed modelling framework can be applied on all levels of spatial granularity and different countries, we consider Ireland as a case study. The network comprises 3440 electoral divisions (EDs) of the Republic of Ireland and 890 superoutput areas (SOAs) for Northern Ireland, which corresponds to local administrative units below the NUTS 3 regions. The local dynamics within each node follows a phenomenological SIRX compartmental model including classes of Susceptibles, Infected, Recovered and Quarantined (X) inspired from Science 368, 742 (2020). For better comparison to empirical data, we extended that model by a class of Deaths. We consider various scenarios including the 5-phase roadmap for Ireland. In addition, as proof of concept, we investigate the effect of dynamic interventions that aim to keep the number of infected below a given threshold. This is achieved by dynamically adjusting containment measures on a national scale, which could also be implemented at a regional (county) or local (ED/SOA) level. We find that - in principle - dynamic interventions are capable to limit the impact of future waves of outbreaks, but on the downside, in the absence of a vaccine, such a strategy can last several years until herd immunity is reached.

A metapopulation network model for the spreading of SARS-CoV-2: Case study for Ireland

We present preliminary results on an all-Ireland network modelling approach to simulate the spreading the Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2), commonly known as the coronavirus. In the model, nodes correspond to locations or communities that are connected by links indicating travel and commuting between different locations. While this proposed modelling framework can be applied on all levels of spatial granularity and different countries, we consider Ireland as a case study. The network comprises 3440 electoral divisions (EDs) of the Republic of Ireland and 890 superoutput areas (SOAs) for Northern Ireland, which corresponds to local administrative units below the NUTS 3 regions. The local dynamics within each node follows a phenomenological SIRX compartmental model including classes of Susceptibles, Infected, Recovered and Quarantined (X) inspired from Science 368, 742 (2020). For better comparison to empirical data, we extended that model by a class of Deaths. We consider various scenarios including the 5-phase roadmap for Ireland. In addition, as proof of concept, we investigate the effect of dynamic interventions that aim to keep the number of infected below a given threshold. This is achieved by dynamically adjusting containment measures on a national scale, which could also be implemented at a regional (county) or local (ED/SOA) level. We find that - in principle - dynamic interventions are capable to limit the impact of future waves of outbreaks, but on the downside, in the absence of a vaccine, such a strategy can last several years until herd immunity is reached.