scholarly journals 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.

2020 ◽  
Author(s):  
Tanishque Propkar Malik
Keyword(s):  
Herd Immunity ◽  
Case Fatality ◽  
Sir Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Case Fatality Ratio ◽  
Stochastic Sir ◽  
Novel Coronavirus ◽  
Stochastic Sir Model ◽  
The Impact

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.

scholarly journals Modelling the spread of American foulbrood in honeybees

2013 ◽  
Vol 10 (88) ◽  
pp. 20130650 ◽  
Author(s):  
Samik Datta ◽  
James C. Bull ◽  
Giles E. Budge ◽  
Matt J. Keeling
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Control Strategies ◽  
Sir Model ◽  
Model Parameters ◽  
American Foulbrood ◽  
Inspection Period ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Impact

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae , that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected ‘occult’ infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.

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

2020 ◽  
Vol 9 (4) ◽  
pp. 944 ◽  
Author(s):  
Kentaro Iwata ◽  
Chisato Miyakoshi
Keyword(s):  
Healthcare Professionals ◽  
Basic Reproductive Number ◽  
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.

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

2021 ◽  
Author(s):  
Salihu Sabiu Musa ◽  
Xueying Wang ◽  
Shi Zhao ◽  
Shudong Li ◽  
Nafiu Hussaini ◽  
...  
Keyword(s):  
Case Fatality ◽  
Well Being ◽  
Mitigation Strategies ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Time Varying ◽  
African Countries ◽  
Awareness Campaigns ◽  
Considerable Impact ◽  
The 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).

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

2020 ◽  
Author(s):  
Kentaro Iwata ◽  
Chisato Miyakoshi
Keyword(s):  
Healthcare Professionals ◽  
Basic Reproductive Number ◽  
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.

scholarly journals The nature of individual heterogeneity shape outbreak dynamics

2021 ◽  
Author(s):  
Baptiste Elie ◽  
Christian Selinger ◽  
Samuel Alizon
Keyword(s):  
Transmission Rate ◽  
Sir Model ◽  
Pathogen Transmission ◽  
Main Driver ◽  
Biological Sources ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Impact ◽  
Parasite Emergence

AbstractIt is now common-place that pathogen transmission during an outbreak can be more heterogeneous than what is commonly assumed, and that it can have major consequences on their dynamics. However, previous studies did not explore the impact of the different biological sources of heterogeneity while controlling for the resulting heterogeneity in the number of secondary cases. In this study, we explore the role of individual variation in infection duration and transmission rate on parasite emergence and spread in a population. We simulate outbreaks using a custom stochastic SIR model, with and without evolution of the parasite. We show that for a given mean, the variance in the number of secondary cases is the main driver of the outbreak probability, with or without evolution, while it does not play a role on the outbreak dynamic once it emerged. On the opposite, a smaller and more realistic variance in the infection duration causes a faster outbreak. It is therefore useful to take into consideration more realistic distributions when modelling infectious diseases outbreaks.

scholarly journals Impact of COVID-19 Variants on the Second Wave in India and Subsequent Discretion of Possibilities of the Third Wave

2021 ◽  
pp. 115-126
Author(s):  
Sudarshan Ramaswamy ◽  
Meera Dhuria ◽  
Sumedha M. Joshi ◽  
Deepa H Velankar
Keyword(s):  
Herd Immunity ◽  
Sir Model ◽  
The Other ◽  
Third Wave ◽  
Focal Points ◽  
Current Analysis ◽  
The Third ◽  
The Impact ◽  
Second Wave ◽  
Insight Into

Introduction: Epidemiological comprehension of the COVID-19 situation in India can be of great help in early prediction of any such indications in other countries and possibilities of the third wave in India as well. It is essential to understand the impact of variant strains in the perspective of the rise in daily cases during the second wave – Whether the rise in cases witnessed is due to the reinfections or the surge is dominated by emergence of mutants/variants and reasons for the same. Overall objective of this study is to predict early epidemiological indicators which can potentially lead to COVID-19 third wave in India. Methodology: We analyzed both the first and second waves of COVID-19 in India and using the data of India’s SARS-CoV-2 genomic sequencing, we segregated the impact of the Older Variant (OV) and the other major variants (VOI / VOC).  Applying Kermack–McKendrick SIR model to the segregated data progression of the epidemic in India was plotted in the form of proportion of people infected. An equation to explain herd immunity thresholds was generated and further analyzed to predict the possibilities of the third wave. Results: Considerable difference in ate of progression of the first and second wave was seen. The study also ascertains that the rate of infection spread is higher in Delta variant and is expected to have a higher threshold (>2 times) for herd immunity as compared to the OV. Conclusion: Likelihood of the occurrence of the third wave seems unlikely based on the current analysis of the situation, however the possibilities cannot be ruled out. Understanding the epidemiological details of the first and second wave helped in understanding the focal points responsible for the surge in cases during the second wave and has given further insight into the future.

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

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 ◽  
Basic Reproductive Number ◽  
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.

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