A Simulation on Potential Secondary Spread of Novel Coronavirus in an Exported Country Using a Stochastic Epidemic SEIR Model

Reproductive Number ◽

Secondary Case ◽

Hospital Visit ◽

Seir Model ◽

Stochastic Epidemic ◽

Novel Coronavirus ◽

The Impact ◽

Multiple Scenarios

Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. On the contrary to ongoing outbreak in China, however, there are limited secondary outbreaks caused by exported case outside the country. We here conducted simulations to estimate the impact of potential secondary outbreaks at a community outside China. Simulations using stochastic SEIR model was conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in total number of persons recovered or removed to be 997 (95% CrI 990-1,000) at day 100 and maximum number of symptomatic infectious patients per day of 335 (95% CrI 232-478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6-7.2). However, with good case scenarios with different parameter led to no secondary case. Altering parameters, especially time to hospital visit could change the impact of secondary outbreak. With this multiple scenarios with different parameters, healthcare professionals might be able to prepare for this viral infection better.

A Simulation on Potential Secondary Spread of Novel Coronavirus in an Exported Country Using a Stochastic Epidemic SEIR Model

Journal of Clinical Medicine ◽

10.3390/jcm9040944 ◽

2020 ◽

Vol 9 (4) ◽

pp. 944 ◽

Cited By ~ 15

Author(s):

Kentaro Iwata ◽

Chisato Miyakoshi

Keyword(s):

Healthcare Professionals ◽

Reproductive Number ◽

Asian Countries ◽

Hospital Visit ◽

Seir Model ◽

Stochastic Epidemic ◽

Novel Coronavirus ◽

The Impact ◽

Multiple Scenarios

Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. Even though it began to spread to many other parts of the world, such as other Asian countries, the Americas, Europe, and the Middle East, the impact of secondary outbreaks caused by exported cases outside China remains unclear. We conducted simulations to estimate the impact of potential secondary outbreaks in a community outside China. Simulations using stochastic SEIR model were conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in the total number of persons recovered or removed to be 997 (95% CrI 990–1000) at day 100 and a maximum number of symptomatic infectious patients per day of 335 (95% CrI 232–478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6–7.2). However, better case scenarios with different parameters led to no secondary cases. Altering parameters, especially time to hospital visit. could change the impact of a secondary outbreak. With these multiple scenarios with different parameters, healthcare professionals might be able to better prepare for this viral infection.

Modelling and Analysis of 2019-nCov Epidemic in India : A study on Attack & Recovery Rate, Basic & Effective Reproductive Number, Herd Immunity Threshold & Case Fatality Ratio of Coronavirus Covid-19 in India.

10.35543/osf.io/cwyeu ◽

2020 ◽

Cited By ~ 2

Author(s):

Tanishque Propkar Malik

Keyword(s):

Herd Immunity ◽

Case Fatality ◽

Sir Model ◽

Reproductive Number ◽

Case Fatality Ratio ◽

Stochastic Sir ◽

Novel Coronavirus ◽

Stochastic Sir Model ◽

Mathematical modelling of any epidemic plays a crucial role in quantifying the impact of such pathogens. This paper focuses on building a Stochastic SIR Model with non-linear parameters (to account for the effect of lockdowns) to gain a broader cognition of the 2019 novel Coronavirus pathogen (2019-nCov), widely known as Covid-19, in India. Such models help in gauging the virulence and fecundity of pathogens. Based on early transmission dynamics the basic reproductive number (R0) is computed to be 1.605. Whereas, effective reproductive number (Rt) is computed to be 4.880 as on 19 March, 2.756 as on 19 April, and 1.995 as on 19 May. Furthermore, the proportion of population that needs to be immunized (through inoculation, recovery, or death) to halt the infection spread is estimated to be 37.69%, ergo, the Herd Immunity Threshold is estimated to be 51.36 crores recoveries, if the Rt remains below 2. Rt is expected to fall below 2, and the Case Fatality Ratio (CFR) to fall to 2.14%, circa early-September (assuming minimal or no medical breakthroughs). The formulated model also provides inferential evidence manifesting the extent to which lockdowns contained the spread of the virus.

AN SEIR MODEL WITH INFECTIOUS LATENT AND A PERIODIC VACCINATION STRATEGY

Mathematical Modelling and Analysis ◽

10.3846/mma.2021.12945 ◽

2021 ◽

Vol 26 (2) ◽

pp. 236-252

Author(s):

Islam A. Moneim

Keyword(s):

Infectious Diseases ◽

Periodic Solutions ◽

Disease Transmission ◽

Vaccination Strategy ◽

Reproductive Number ◽

New Wave ◽

Globally Asymptotically Stable ◽

Seir Model ◽

An SEIR epidemic model with a nonconstant vaccination strategy is studied. This SEIR model has two disease transmission rates β1 and β2 which imitate the fact that, for some infectious diseases, a latent person can pass the disease into a susceptible one. Here we study the spread of some childhood infectious diseases as good examples of diseases with infectious latent. We found that our SEIR model has a unique disease free solution (DFS). A lower bound and an upper bound of the basic reproductive number, R0 are estimated. We show that, the DFS is globally asymptotically stable when and unstable if Computer simulations have been conducted to show that non trivial periodic solutions are possible. Moreover the impact of the contact rate between the latent and the susceptibles is simulated. Different periodic solutions with different periods including one, two and three years, are obtained. These results give a clearer view for the decision makers to know how and when they should take action against a possible new wave of these infectious diseases. This action is mainly, applying a suitable dose of vaccination just before a severe peak of infection occurs.

Modeling and stability analysis of the spread of novel coronavirus disease COVID-19

International Journal of Biomathematics ◽

10.1142/s1793524521500352 ◽

2021 ◽

pp. 2150035

Author(s):

A. George Maria Selvam ◽

Jehad Alzabut ◽

D. Abraham Vianny ◽

Mary Jacintha ◽

Fatma Bozkurt Yousef

Keyword(s):

Fractional Order ◽

Disease Transmission ◽

Equilibrium Points ◽

Sufficient Conditions ◽

Phase Portraits ◽

Transmission Model ◽

Reproductive Number ◽

Discrete Version ◽

Novel Coronavirus

Towards the end of 2019, the world witnessed the outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (COVID-19), a new strain of coronavirus that was unidentified in humans previously. In this paper, a new fractional-order Susceptible–Exposed–Infected–Hospitalized–Recovered (SEIHR) model is formulated for COVID-19, where the population is infected due to human transmission. The fractional-order discrete version of the model is obtained by the process of discretization and the basic reproductive number is calculated with the next-generation matrix approach. All equilibrium points related to the disease transmission model are then computed. Further, sufficient conditions to investigate all possible equilibria of the model are established in terms of the basic reproduction number (local stability) and are supported with time series, phase portraits and bifurcation diagrams. Finally, numerical simulations are provided to demonstrate the theoretical findings.

SE2IR Invest Market Rumor Spreading Model Considering Hesitating Mechanism

Journal of Systems Science and Information ◽

10.21078/jssi-2019-054-16 ◽

2019 ◽

Vol 7 (1) ◽

pp. 54-69 ◽

Cited By ~ 3

Author(s):

Hongxing Yao ◽

Xiangyang Gao

Keyword(s):

Mean Field ◽

Reproductive Number ◽

Field Equations ◽

Rumor Spreading ◽

Immunization Strategy ◽

Scale Free ◽

Spreading Model ◽

Mean Field Equations ◽

Abstract According to the actual situation of investor network, a SE2IR rumor spreading model with hesitating mechanism is proposed, and the corresponding mean-field equations is obtained on scale-free network. In this paper, we first combine the theory of spreading dynamics and find out the basic reproductive number R0. And then analyzes the stability of the rumor-free equilibrium and the final rumor size. Finally, we discuss random immune strategies and target immune strategies for the rumor spreading, respectively. Through numerical simulation, we can draw the following conclusions: Reducing the fuzziness and attractiveness of invest market rumor can effectively reduce the impact of rumor. And the target immunization strategy is more effective than the random immunization strategy for the communicators in the invest investor network.

HEPATITIS C VIRUS AND INTRAVENOUS DRUG MISUSE: A MODELING APPROACH

International Journal of Biomathematics ◽

10.1142/s1793524514500065 ◽

2014 ◽

Vol 07 (01) ◽

pp. 1450006 ◽

Cited By ~ 2

Author(s):

STEADY MUSHAYABASA ◽

CLAVER P. BHUNU

Keyword(s):

Hepatitis C Virus ◽

Hepatitis C ◽

Steady States ◽

Transmission Dynamics ◽

Intravenous Drug ◽

Drug Misuse ◽

Dynamical Analysis ◽

Reproductive Number ◽

Hepatitis C virus (HCV) is a blood-borne infection that can lead to progressive liver failure, cirrhosis, hepatocellular carcinoma and death. A deterministic mathematical model for assessing the impact of daily intravenous drug misuse on the transmission dynamics of HCV is presented and analyzed. A threshold quantity known as the reproductive number has been computed. Stability of the steady states has been investigated. The dynamical analysis reveals that the model has globally asymptotically stable steady states. The impact of daily intravenous drug misuse on the transmission dynamics of HCV has been discussed through the basic reproductive number and numerical simulations.

Analysis of the COVID-19 epidemic in french overseas department Mayotte based on a modified deterministic and stochastic SEIR model

10.1101/2020.04.15.20062752 ◽

2020 ◽

Author(s):

Solym Mawaki Manou-Abi ◽

Julien Balicchi

Keyword(s):

Transmission Rate ◽

Control Measure ◽

Exponential Growth Phase ◽

The Novel ◽

Rate Parameter ◽

Seir Model ◽

Stochastic Epidemic ◽

Access To Water ◽

Novel Coronavirus ◽

Death Cases

AbstractIn order to anticipate a future trends in the development of the novel coronavirus COVID-19 epidemic started early at march 13, in the french overseas department Mayotte, we consider in this paper a modified deterministic and stochastic epidemic model. The model divides the total population into several possible states or compartment: susceptible (S), exposed (E) infected and being under an incubation period, infected (I) being infectious, simple or mild removed RM, severe removed (including hospitalized) RS and death cases (D). The adding of the two new compartment RM and RS are driven by data which together replace the original R compartment in the classical SEIR model.We first fit the constant transmission rate parameter to the epidemic data in Mayotte during an early exponential growth phase using an algorithm with a package of the software R and based on a Maximum Likewood estimator. This allows us to predict the epidemic without any control in order to understand how the control measure and public policies designed are having the desired impact of controlling the epidemic. To do this, we introduce a temporally varying decreasing transmission rate parameter with a control or quarantine parameter q. Then we pointed out some values of q to maintain control which is critical in Mayotte given the fragility of its health infrastructure and the significant fraction of the population without access to water.

The effects of the clinical symptoms pneumonia-confirmation strategy of the COVID-19 epidemic in Wuhan, China

10.21203/rs.3.rs-28619/v1 ◽

2020 ◽

Author(s):

Yanjin Wang ◽

Pei Wang ◽

Shudao Zhang ◽

Hao Pan

Keyword(s):

Turning Point ◽

Clinical Symptoms ◽

Transmission Rate ◽

Reproductive Number ◽

The Novel ◽

Wuhan City ◽

Start Date ◽

Rapid Spread ◽

Novel Coronavirus

Abstract Motivated by the quick control in Wuhan, China, and the rapid spread in other countries of COVID-19, we investigate the questions that what is the turning point in Wuhan by quantifying the variety of basic reproductive number after the lockdown city. The answer may help the world to control the COVID-19 epidemic. A modified SEIR model is used to study the COVID-19 epidemic in Wuhan city. Our model is calibrated by the hospitalized cases. The modeling result gives out that the means of basic reproductive numbers are 1.5517 (95% CI 1.1716-4.4283) for the period from Jan 25 to Feb 11, 2020, and 0.4738(95% CI 0.0997-0.8370) for the period from Feb 12 to Mar 10. The transmission rate fell after Feb 12, 2020 as a result of China’s COVID-19 strategy of keeping society distance and the medical support from all China, but principally because of the clinical symptoms to be used for the novel coronavirus pneumonia (NCP) confirmation in Wuhan since Feb 12, 2020. Clinical diagnosis can quicken up NCP-confirmation such that the COVID-19 patients can be isolated without delay. So the clinical symptoms pneumonia-confirmation is the turning point of the COVID-19 battle of Wuhan. The measure of clinical symptoms pneumonia-confirmation in Wuhan has delayed the growth and reduced size of the COVID-19 epidemic, decreased the peak number of the hospitalized cases by 96% in Wuhan. Our modeling also indicates that the earliest start date of COVID-19 in Wuhan may be Nov 2, 2019.

Estimating the Prevalence of Asymptomatic COVID-19 Cases and Their Contribution in Transmission - Using Henan Province, China, as an Example

Frontiers in Medicine ◽

10.3389/fmed.2021.591372 ◽

2021 ◽

Vol 8 ◽

Author(s):

Chunyu Li ◽

Yuchen Zhu ◽

Chang Qi ◽

Lili Liu ◽

Dandan Zhang ◽

...

Keyword(s):

Severe Acute Respiratory Syndrome ◽

Early Stage ◽

Henan Province ◽

Substantial Proportion ◽

Reproductive Number ◽

The World ◽

Asymptomatic Infections ◽

Novel Coronavirus

Background: Novel coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-COV-2), is now sweeping across the world. A substantial proportion of infections only lead to mild symptoms or are asymptomatic, but the proportion and infectivity of asymptomatic infections remains unknown. In this paper, we proposed a model to estimate the proportion and infectivity of asymptomatic cases, using COVID-19 in Henan Province, China, as an example.Methods: We extended the conventional susceptible-exposed-infectious-recovered model by including asymptomatic, unconfirmed symptomatic, and quarantined cases. Based on this model, we used daily reported COVID-19 cases from January 21 to February 26, 2020, in Henan Province to estimate the proportion and infectivity of asymptomatic cases, as well as the change of effective reproductive number, Rt.Results: The proportion of asymptomatic cases among COVID-19 infected individuals was 42% and the infectivity was 10% that of symptomatic ones. The basic reproductive number R0 = 2.73, and Rt dropped below 1 on January 31 under a series of measures.Conclusion: The spread of the COVID-19 epidemic was rapid in the early stage, with a large number of asymptomatic infected individuals having relatively low infectivity. However, it was quickly brought under control with national measures.

The heterogeneous severity of COVID-19 in African countries: A modeling approach

10.21203/rs.3.rs-426664/v1 ◽

2021 ◽

Author(s):

Salihu Sabiu Musa ◽

Xueying Wang ◽

Shi Zhao ◽

Shudong Li ◽

Nafiu Hussaini ◽

...

Keyword(s):

Case Fatality ◽

Well Being ◽

Mitigation Strategies ◽

Reproductive Number ◽

Time Varying ◽

African Countries ◽

Awareness Campaigns ◽

Considerable Impact ◽

Abstract Background: The COVID-19 pandemic has had a considerable impact on global health and economics. The impact in African countries has not been investigated through fitting epidemic models to the reported COVID-19 deaths.Method: We downloaded data for the twelve most affected countries with the highest cumulative COVID-19 deaths to estimate the time-varying basic reproductive number (R0(t)) and infection attack rate (IAR). We developed a simple epidemic model and fitted the model to reported COVID-19 deaths in twelve African countries using iterated filtering and allowing a flexible transmission rate.Results: We observed high heterogeneity in the case-fatality rate across countries, which may be due to different reporting or testing efforts. South Africa, Tunisia, and Libya were affected most strongly, exhibiting a relatively higher(R0(t)) and infection attack rate.Conclusion: To effectively control the spread of COVID-19 epidemics in Africa, there is a need to consider other mitigation strategies (such as improvements in socioeconomic well-being, healthcare systems, the water supply, and awareness campaigns).