Estimating the reproduction number and forecasting the impact of COVID-19 in Kuwait using a modified compartmental epidemiological model

Abstract A modified compartmental epidemic model was developed to simulate the state of Kuwait protocol in fighting COVID-19 pandemic. The next generation matrix method was used to drive an expression for the basic reproduction number, R0. Basic and effective reproduction numbers were calculated using data from the intrinsic growth rate of the confirmed COVID-19 cases. R0 was found to be 2.18. Three scenarios that varied by effective reproduction number were used to estimate the future course of the disease: a high value of R = 1.98, a middle value of R = 1.62, and a low value of R = 1.2. The maximum number of beds required in general hospitals in each scenario were estimated at 141 184, 85 341, and 16 412, respectively. For intensive care units, the estimated numbers of beds required were 16 461, 9 645, and 1788. Maximum deaths also varied and were estimated to be 29 202, 23 973, and 11 565. For the maximum value of R, it is estimated to peak on August 27, 2020. For the middle value of R, it is estimated to peak on September 20, 2020. For the minimum value of R, it is estimated to peak on December 21, 2020.

Understanding the dynamics of Ebola epidemics

Epidemiology and Infection ◽

10.1017/s0950268806007217 ◽

2006 ◽

Vol 135 (4) ◽

pp. 610-621 ◽

Cited By ~ 202

Author(s):

J. LEGRAND ◽

R. F. GRAIS ◽

P. Y. BOELLE ◽

A. J. VALLERON ◽

A. FLAHAULT

Keyword(s):

Democratic Republic ◽

Reproduction Number ◽

Democratic Republic Of Congo ◽

Hospitalization Rate ◽

Control Measures ◽

Epidemic Size ◽

Using Data ◽

The Impact ◽

The Basic Reproduction Number ◽

Key Parameter

SUMMARYEbola is a highly lethal virus, which has caused at least 14 confirmed outbreaks in Africa between 1976 and 2006. Using data from two epidemics [in Democratic Republic of Congo (DRC) in 1995 and in Uganda in 2000], we built a mathematical model for the spread of Ebola haemorrhagic fever epidemics taking into account transmission in different epidemiological settings. We estimated the basic reproduction number (R0) to be 2·7 (95% CI 1·9–2·8) for the 1995 epidemic in DRC, and 2·7 (95% CI 2·5–4·1) for the 2000 epidemic in Uganda. For each epidemic, we quantified transmission in different settings (illness in the community, hospitalization, and traditional burial) and simulated various epidemic scenarios to explore the impact of control interventions on a potential epidemic. A key parameter was the rapid institution of control measures. For both epidemic profiles identified, increasing hospitalization rate reduced the predicted epidemic size.

Impact of anti-virus software on computer virus dynamical behavior

International Journal of Modern Physics C ◽

10.1142/s0129183114400105 ◽

2014 ◽

Vol 25 (05) ◽

pp. 1440010 ◽

Cited By ~ 1

Author(s):

Mei Sun ◽

Dandan Li ◽

Dun Han ◽

Changsheng Jia

Keyword(s):

Mathematical Model ◽

Lyapunov Function ◽

Reproduction Number ◽

Dynamical Behavior ◽

Computer Virus ◽

Stability Conditions ◽

Next Generation Matrix ◽

The Stability ◽

The Impact ◽

The impact of anti-virus software on the spreading of computer virus is investigated via developing a mathematical model in this paper. Considering the anti-virus software may not be effective, as it may be an outdated version, and then the computers may be infected with a reduced incidence rate. According to the method of next generation matrix, the basic reproduction number is derived. By introducing appropriate Lyapunov function and the Routh stability criterion, acquiring the stability conditions of the virus-free equilibrium and virus equilibrium. The effect of anti-virus software and disconnecting rate on the spreading of virus are also analyzed. When combined with the numerical results, a set of suggestions are put forward for eradicating virus effectively.

COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling (Preprint)

10.2196/preprints.23997 ◽

2020 ◽

Author(s):

Eduardo Atem De Carvalho ◽

Rogerio Atem De Carvalho

Keyword(s):

New York ◽

Reproduction Number ◽

Moving Average ◽

Real Data ◽

Time Dependent ◽

Initial Value ◽

Health Authorities ◽

Reproduction Numbers ◽

Effect Estimation ◽

The Impact

BACKGROUND Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. OBJECTIVE This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. METHODS The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. RESULTS Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. CONCLUSIONS We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent, incubation period-independent Reproduction Numbers (Rt). We also demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

Advances in Difference Equations ◽

10.1186/s13662-020-03081-2 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Shuai Yang ◽

Haijun Jiang ◽

Cheng Hu ◽

Juan Yu ◽

Jiarong Li

Keyword(s):

Lyapunov Method ◽

Reproduction Number ◽

Model Parameters ◽

Rumor Spreading ◽

Spreading Model ◽

Reductio Ad Absurdum ◽

The Stability ◽

The Impact ◽

Theoretical Results ◽

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

The effects of non-pharmaceutical interventions on SARS-CoV-2 transmission in different socioeconomic populations in Kuwait: a modeling study

BMC Public Health ◽

10.1186/s12889-021-10984-6 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Fatima Khadadah ◽

Abdullah A. Al-Shammari ◽

Ahmad Alhashemi ◽

Dari Alhuwail ◽

Bader Al-Saif ◽

...

Keyword(s):

Disease Transmission ◽

Reproduction Number ◽

Transmission Model ◽

Socioeconomic Groups ◽

Before And After ◽

Cross Transmission ◽

Community Transmission ◽

The Impact ◽

Pharmaceutical Interventions ◽

Abstract Background Aggressive non-pharmaceutical interventions (NPIs) may reduce transmission of SARS-CoV-2. The extent to which these interventions are successful in stopping the spread have not been characterized in countries with distinct socioeconomic groups. We compared the effects of a partial lockdown on disease transmission among Kuwaitis (P1) and non-Kuwaitis (P2) living in Kuwait. Methods We fit a modified metapopulation SEIR transmission model to reported cases stratified by two groups to estimate the impact of a partial lockdown on the effective reproduction number ($$ {\mathcal{R}}_e $$ R e ). We estimated the basic reproduction number ($$ {\mathcal{R}}_0 $$ R 0 ) for the transmission in each group and simulated the potential trajectories of an outbreak from the first recorded case of community transmission until 12 days after the partial lockdown. We estimated $$ {\mathcal{R}}_e $$ R e values of both groups before and after the partial curfew, simulated the effect of these values on the epidemic curves and explored a range of cross-transmission scenarios. Results We estimate $$ {\mathcal{R}}_e $$ R e at 1·08 (95% CI: 1·00–1·26) for P1 and 2·36 (2·03–2·71) for P2. On March 22nd, $$ {\mathcal{R}}_e $$ R e for P1 and P2 are estimated at 1·19 (1·04–1·34) and 1·75 (1·26–2·11) respectively. After the partial curfew had taken effect, $$ {\mathcal{R}}_e $$ R e for P1 dropped modestly to 1·05 (0·82–1·26) but almost doubled for P2 to 2·89 (2·30–3·70). Our simulated epidemic trajectories show that the partial curfew measure greatly reduced and delayed the height of the peak in P1, yet significantly elevated and hastened the peak in P2. Modest cross-transmission between P1 and P2 greatly elevated the height of the peak in P1 and brought it forward in time closer to the peak of P2. Conclusion Our results indicate and quantify how the same lockdown intervention can accentuate disease transmission in some subpopulations while potentially controlling it in others. Any such control may further become compromised in the presence of cross-transmission between subpopulations. Future interventions and policies need to be sensitive to socioeconomic and health disparities.

Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

Abstract and Applied Analysis ◽

10.1155/2014/841367 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Jianping Wang ◽

Shujing Gao ◽

Yueli Luo ◽

Dehui Xie

Keyword(s):

Reproduction Number ◽

Logistic Growth ◽

Threshold Dynamics ◽

Global Dynamics ◽

Globally Asymptotically Stable ◽

Linear Integral ◽

The Impact ◽

Disease Free ◽

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction numberR0which is defined through the spectral radius of a linear integral operator. IfR0< 1, then the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.

Data-driven tools for assessing and combating COVID-19 outbreaks in Brazil based on analytics and statistical methods

10.22514/sv.2021.253 ◽

2021 ◽

Keyword(s):

Data Analytics ◽

Exploratory Data Analysis ◽

Reproduction Number ◽

Healthcare Systems ◽

Regional Level ◽

Data Driven ◽

Effective Response ◽

Reproduction Numbers ◽

Exploratory Data ◽

Using Data

The COVID-19 pandemic is one of the worst public health crises in Brazil and the world that has ever been faced. One of the main challenges that the healthcare systems have when decision-making is that the protocols tested in other epidemics do not guarantee success in controlling the spread of COVID-19, given its complexity. In this context, an effective response to guide the competent authorities in adopting public policies to fight COVID-19 depends on thoughtful analysis and effective data visualization, ideally based on different data sources. In this paper, we discuss and provide tools that can be helpful using data analytics to respond to the COVID-19 outbreak in Recife, Brazil. We use exploratory data analysis and inferential study to determine the trend changes in COVID-19 cases and their effective or instantaneous reproduction numbers. According to the data obtained of confirmed COVID-19 cases disaggregated at a regional level in this zone, we note a heterogeneous spread in most megaregions in Recife, Brazil. When incorporating quarantines decreed, effectiveness is detected in the regions. Our results indicate that the measures have effectively curbed the spread of the disease in Recife, Brazil. However, other factors can cause the effective reproduction number to not be within the expected ranges, which must be further studied.

A THEORETICAL ASSESSMENT OF THE EFFECTS OF DISTRIBUTED DELAY ON THE TRANSMISSION DYNAMICS OF HEPATITIS B

Journal of Biological System ◽

10.1142/s0218339015500229 ◽

2015 ◽

Vol 23 (03) ◽

pp. 423-455

Author(s):

P. MOUOFO TCHINDA ◽

JEAN JULES TEWA ◽

BOULECHARD MEWOLI ◽

SAMUEL BOWONG

Keyword(s):

Drug Therapy ◽

Hepatitis B ◽

Disease Transmission ◽

Time Delays ◽

Reproduction Number ◽

Distributed Delay ◽

Global Dynamics ◽

The Impact ◽

In this paper, we investigate the global dynamics of a system of delay differential equations which describes the interaction of hepatitis B virus (HBV) with both liver and blood cells. The model has two distributed time delays describing the time needed for infection of cell and virus replication. We also include the efficiency of drug therapy in inhibiting viral production and the efficiency of drug therapy in blocking new infection. We compute the basic reproduction number and find that increasing delays will decrease the value of the basic reproduction number. We study the sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Our analysis reveals that the model exhibits the phenomenon of backward bifurcation (where a stable disease-free equilibrium (DFE) co-exists with a stable endemic equilibrium when the basic reproduction number is less than unity). Numerical simulations are presented to evaluate the impact of time-delays on the prevalence of the disease.

Seasonality Impact on the Transmission Dynamics of Tuberculosis

Computational and Mathematical Methods in Medicine ◽

10.1155/2016/8713924 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Yali Yang ◽

Chenping Guo ◽

Luju Liu ◽

Tianhua Zhang ◽

Weiping Liu

Keyword(s):

Reproduction Number ◽

Autonomous Systems ◽

Positive Periodic Solution ◽

Transmission Dynamics ◽

Uniform Persistence ◽

Globally Asymptotically Stable ◽

The Impact ◽

Disease Free ◽

The statistical data of monthly pulmonary tuberculosis (TB) incidence cases from January 2004 to December 2012 show the seasonality fluctuations in Shaanxi of China. A seasonality TB epidemic model with periodic varying contact rate, reactivation rate, and disease-induced death rate is proposed to explore the impact of seasonality on the transmission dynamics of TB. Simulations show that the basic reproduction number of time-averaged autonomous systems may underestimate or overestimate infection risks in some cases, which may be up to the value of period. The basic reproduction number of the seasonality model is appropriately given, which determines the extinction and uniform persistence of TB disease. If it is less than one, then the disease-free equilibrium is globally asymptotically stable; if it is greater than one, the system at least has a positive periodic solution and the disease will persist. Moreover, numerical simulations demonstrate these theorem results.

Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate

Abstract and Applied Analysis ◽

10.1155/2014/586035 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Yu Ji ◽

Muxuan Zheng

Keyword(s):

Viral Infection ◽

Incidence Rate ◽

Reproduction Number ◽

Infection Model ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Reproduction Numbers ◽

The Basic Reproduction Number ◽

General Standard

The basic viral infection models, proposed by Nowak et al. and Perelson et al., respectively, have been widely used to describe viral infection such as HBV and HIV infection. However, the basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection, which seems not to be reasonable. In this paper, we formulate an amended model with a general standard incidence rate. The basic reproduction number of the amended model is independent of total cells of the host’s organ. When the basic reproduction numberR0<1, the infection-free equilibrium is globally asymptotically stable and the virus is cleared. Moreover, ifR0>1, then the endemic equilibrium is globally asymptotically stable and the virus persists in the host.