scholarly journals COVID-19 Pandemic in India: A Mathematical Model Study

2020 ◽  
Author(s):  
Sudhanshu Kumar Biswas ◽  
Jayanta Kumar Ghosh ◽  
Susmita Sarkar ◽  
Uttam Ghosh
Keyword(s):  
Population Density ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Virus Disease ◽  
Control Measures ◽  
High Population ◽  
Model Parameters ◽  
High Population Density ◽  
Corona Virus ◽  
Very High

The present novel corona virus (2019-nCoV) infection has created a global emergency situation by spreading all over the world in a large scale within very short time period. The infection induced death rate is also very high. There is no vaccine or anti-viral medicine for such infection. So at this moment a major worldwide problem is that how we can control this pandemic. On the other hand, India is a high population density country, where the corona virus disease (COVID-19) has started to spread from $1^{st}$ week of March, 2020 in a significant number of COVID-19 positive cases. Due to this high population density human to human social contact rate is very high in India. So control of the pandemic COVID-19 in early stage is very urgent and challenging problem. Mathematical models are employed in this paper to study the COVID-19 dynamics, to identify the influential parameters and to find the proper prevention strategies to reduce the outbreak size. In this work, we have formulated a deterministic compartmental model to study the spreading of COVID-19 and estimated the model parameters by fitting the model with reported data of ongoing pandemic in India. Sensitivity analysis has been done to identify the key model parameters. The basic reproduction number has been estimated from actual data and the effective basic reproduction number has been studied on the basis of reported cases. Some effective preventive measures and their impacts on the disease dynamics have also been studied. Future trends of the disease transmission has been Predicted from our model with some control measures. Finally, the positive measures to control the disease have been summarized.

scholarly journals Mathematical Model of the Transmission Dynamics of Corona Virus Disease (COVID-19) and Its Control

2021 ◽  
pp. 69-88
Author(s):  
Atokolo William ◽  
Omale David ◽  
Bashir Sezuo Tenuche ◽  
Olayemi Kehinde Samuel ◽  
Daniel Musa Alih ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium State ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Virus Disease ◽  
Control Measure ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Corona Virus ◽  
The Basic Reproduction Number

This work is aimed at formulating a mathematical model for the transmission dynamics and control of corona virus disease in a population. The Disease Free Equilibrium state of the model was determined and shown to be locally asymptotically stable. The Endemic Equilibrium state of the model was also established and proved to be locally asymptotically stable using the trace and determinant method, after which we determined the basic reproduction number ( ) of the model using the next generation method. When ( ), the disease is wiped out of a population, but if ( ), the disease invades such population. Local sensitivity analysis result shows that the rate at which the exposed are quarantined ( ), the rate at which the infected are isolated ( ), the rate at which the quarantined are isolated ( ), and the treatment rate ( ) should be targeted by the control intervention strategies as an increase in the values of these parameters (  and ) will reduce the basic reproduction number  ( ) of the COVID-19 and as such will eliminate the disease from the population with time. Numerical simulation of the model shows that the disease will be eradicated with time when enlightenment control measure for the susceptible individuals to observe social distance, frequent use of hand sanitizers, covering of mouth when coughing or sneezing are properly observed. Moreso, increasing the rates at which the suspected and confirmed cases of COVID-19 are quarantined and isolated respectively reduce the spread of the global pandemic.

scholarly journals A Mathematical Model Approach for Prevention and Intervention Measures of the COVID–19 Pandemic in Uganda

2020 ◽  
Author(s):  
Fulgensia Kamugisha Mbabazi ◽  
Yahaya Gavamukulya ◽  
Richard Awichi ◽  
Peter Olupot–Olupot ◽  
Samson Rwahwire ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Virus Disease ◽  
Transmission Rate ◽  
Control Strategies ◽  
Social Distancing ◽  
Corona Virus ◽  
The Impact ◽  
The Basic Reproduction Number

AbstractThe human–infecting corona virus disease (COVID–19) caused by the novel severe acute respiratory syndrome corona virus 2 (SARS–CoV–2) was declared a global pandemic on March 11th, 2020. Current human deaths due to the infection have raised the threat globally with only 1 African country free of Virus (Lesotho) as of May 6th, 2020. Different countries have adopted different interventions at different stages of the outbreak, with social distancing being the first option while lock down the preferred option for flattening the curve at the peak of the pandemic. Lock down is aimed at adherence to social distancing, preserve the health system and improve survival. We propose a Susceptible–Exposed–Infected–Expected recoveries (SEIR) mathematical model to study the impact of a variety of prevention and control strategies Uganda has applied since the eruption of the pandemic in the country. We analyze the model using available data to find the infection–free, endemic/infection steady states and the basic reproduction number. In addition, a sensitivity analysis done shows that the transmission rate and the rate at which persons acquire the virus, have a positive influence on the basic reproduction number. On other hand the rate of evacuation by rescue ambulance greatly reduces the reproduction number. The results have potential to inform the impact and effect of early strict interventions including lock down in resource limited settings and social distancing.

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

scholarly journals What can the ideal gas say about global pandemics? Reinterpreting the basic reproduction number

2020 ◽  
Author(s):  
Bradley M Dickson
Keyword(s):  
Random Walk ◽  
Population Density ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
The United States ◽  
Ideal Gas ◽  
Parameter Estimates ◽  
Public Data ◽  
The Basic Reproduction Number ◽  
The Ideal

Through analysis of the ideal gas, we construct a random walk that on average matches the standard susceptible-infective-removed (SIR) model. We show that the most widely referenced parameter, the 'basic reproduction number' (R0), is fundamentally connected to the relative odds of increasing or decreasing the infectives population. As a consequence, for R0 > 1 the probability that no outbreak occurs is 1/R0. In stark contrast to a deterministic SIR, when R0 = 1.5 the random walk has a 67% chance of avoiding outbreak. Thus, an alternative, probabilistic, interpretation of R0 arises, which provides a novel estimate of the critical population density γ/r without fitting SIR models. We demonstrate that SARS-CoV2 in the United States is consistent with our model and attempt an estimate of γ/r. In doing so, we uncover a significant source of bias in public data reporting. Data are aggregated on political boundaries, which bear no concern for dispersion of population density. We show that this introduces bias in fits and parameter estimates, a concern for understanding fundamental virus parameters and for policy making. Anonymized data at the resolution required for contact tracing would afford access to γ/r without fitting. The random walk SIR developed here highlights the intuition that any epidemic is stochastic and recovers all the key parameter values noted by Kermack and McKendrick in 1927.

scholarly journals Recruitment sex ratios in gray-tailed voles (Microtus canicaudus) in response to density, sex ratio, and season

2003 ◽  
Vol 81 (8) ◽  
pp. 1306-1311 ◽  
Author(s):  
Monica L Bond ◽  
Jerry O Wolff ◽  
Sven Krackow
Keyword(s):  
Population Density ◽  
Sex Ratio ◽  
Resource Competition ◽  
Sex Ratios ◽  
Female Offspring ◽  
High Population ◽  
Reproductive Value ◽  
High Population Density ◽  
Adult Sex Ratio ◽  
Sex Ratio Adjustment

We tested predictions associated with three widely used hypotheses for facultative sex-ratio adjustment of vertebrates using eight enclosed populations of gray-tailed voles, Microtus canicaudus. These were (i) the population sex ratio hypothesis, which predicts that recruitment sex ratios should oppose adult sex-ratio skews, (ii) the local resource competition hypothesis, which predicts female-biased recruitment at low adult population density and male-biased recruitment at high population density, and (iii) the first cohort advantage hypothesis, which predicts that recruitment sex ratios should be female biased in the spring and male biased in the autumn. We monitored naturally increasing population densities with approximately equal adult sex ratios through the spring and summer and manipulated adult sex ratios in the autumn and measured subsequent sex ratios of recruits. We did not observe any significant sex-ratio adjustment in response to adult sex ratio or high population density; we did detect an influence of time within the breeding season, with more female offspring observed in the spring and more male offspring observed in the autumn. Significant seasonal increases in recruitment sex ratios indicate the capacity of female gray-tailed voles to manipulate their offspring sex ratios and suggest seasonal variation in the relative reproductive value of male and female offspring to be a regular phenomenon.

Aggregations of masked shrews ( Sorex cinereus ): density-related mating behavior? / Agrégation de musaraignes masquées ( Sorex cinereus ): accouplement relatif à la densité de la population?

Mammalia ◽  
2006 ◽  
Vol 70 (1-2) ◽  
Author(s):  
Thomas J. Maier ◽  
Katherine L. Doyle
Keyword(s):  
Population Density ◽  
Mating Behavior ◽  
High Population ◽  
High Population Density ◽  
Genetic Analyses ◽  
Highly Active ◽  
Sorex Cinereus

AbstractLarge aggregations of shrews have been reported and various explanations offered for this seemingly rare behavior; however, there has been little evidence to support any particular interpretation. We observed two small aggregations of highly active vocalizing Sorex cinereus while performing wildlife surveys in forested habitats in central Massachusetts, USA. These observations, in conjunction with a review of other reports, including genetic analyses, strongly suggest that such aggregations of adult Sorex are associated with mating behavior, more readily observed during periods of high population density. Published accounts of such behavior may be rare because primarily large aggregations have been reported; however, smaller breeding aggregations may be common.

Analysis of steroid hormone levels in female mice at high population density

1998 ◽  
Vol 64 (4) ◽  
pp. 529-533 ◽  
Author(s):  
John C Chapman ◽  
John J Christian ◽  
Mary Ann Pawlikowski ◽  
Sandra D Michael
Keyword(s):  
Population Density ◽  
Steroid Hormone ◽  
High Population ◽  
High Population Density ◽  
Hormone Levels ◽  
Female Mice
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