scholarly journals Collocation of Next-Generation Operators for Computing the Basic Reproduction Number of Structured Populations

2020 ◽  
Vol 85 (2) ◽  
Author(s):  
Dimitri Breda ◽  
Toshikazu Kuniya ◽  
Jordi Ripoll ◽  
Rossana Vermiglio
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Structured Populations ◽  
Infinite Dimensional ◽  
Structured Population ◽  
Full Analysis ◽  
Collocation Approach ◽  
The One ◽  
Rigorous Error ◽  
The Basic Reproduction Number

AbstractWe contribute a full analysis of theoretical and numerical aspects of the collocation approach recently proposed by some of the authors to compute the basic reproduction number of structured population dynamics as spectral radius of certain infinite-dimensional operators. On the one hand, we prove under mild regularity assumptions on the models coefficients that the concerned operators are compact, so that the problem can be properly recast as an eigenvalue problem thus allowing for numerical discretization. On the other hand, we prove through detailed and rigorous error and convergence analyses that the method performs the expected spectral accuracy. Several numerical tests validate the proposed analysis by highlighting diverse peculiarities of the investigated approach.

scholarly journals On the basic reproduction number in continuously structured populations

2020 ◽  
Vol 44 (1) ◽  
pp. 799-812 ◽  
Author(s):  
Carles Barril ◽  
Àngel Calsina ◽  
Sílvia Cuadrado ◽  
Jordi Ripoll
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Structured Populations ◽  
The Basic Reproduction Number

scholarly journals Could Deficiencies in South African Data Be the Explanation for Its Early SARS-CoV-2 Peak?

2020 ◽  
Author(s):  
Simon John Childs
Keyword(s):  
South African ◽  
Basic Reproduction Number ◽  
External Factor ◽  
Reproduction Number ◽  
Profound Change ◽  
Multiplicative Factor ◽  
Early Peak ◽  
The One ◽  
The Basic Reproduction Number

The SARS-CoV-2 pandemic peaked very early in comparison to the thresholds predicted by an analysis of prior lockdown regimes. The most convenient explanation is that some, external factor changed the value of the basic reproduction number, r0; and there certainly are arguments for this. Other factors could, nonetheless, have played a role. This research attempts to reconcile the observed peak with the thresholds predicted by lockdown regimes similar to the one in force at the time. It contemplates the effect of two, different, hypothetical errors in the data: The first is that the true level of infection has been underestimated by a multiplicative factor, while the second is that of an imperceptible, pre-existing, immune fraction of the population. While it is shown that it certainly is possible to manufacture the perception of an early peak as extreme as the one observed, solely by way of these two phenomena, the values need to be fairly high. The phenomena would not, by any measure, be insignificant. It also remains an inescapable fact that the early peak in infections coincided with a fairly profound change in r0; in all the contemplated scenarios of data-deficiency.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

scholarly journals Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Dipo Aldila ◽  
Brenda M. Samiadji ◽  
Gracia M. Simorangkir ◽  
Sarbaz H. A. Khosnaw ◽  
Muhammad Shahzad
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccination Strategy ◽  
Vaccination Rate ◽  
Rapid Testing ◽  
Social Distancing ◽  
Rapid Spread ◽  
Vaccine Potential ◽  
The Basic Reproduction Number

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.

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 Mathematical analysis of a within-host model of SARS-CoV-2

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bhagya Jyoti Nath ◽  
Kaushik Dehingia ◽  
Vishnu Narayan Mishra ◽  
Yu-Ming Chu ◽  
Hemanta Kumar Sarmah
Keyword(s):  
Stability Analysis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Basic Reproduction Ratio ◽  
Viral Kinetics ◽  
Reproduction Ratio ◽  
Biological Implication ◽  
Infection Models ◽  
Kinetics Of ◽  
The Basic Reproduction Number

AbstractIn this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper “The within-host viral kinetics of SARS-CoV-2” published in (Math. Biosci. Eng. 17(4):2853–2861, 2020). Important properties of the model, like nonnegativity of solutions and their boundedness, are established. Also, we have calculated the basic reproduction number which is an important parameter in the infection models. From stability analysis of the model, it is found that stability of the biologically feasible steady states are determined by the basic reproduction number $(\chi _{0})$ ( χ 0 ) . Numerical simulations are done in order to substantiate analytical results. A biological implication from this study is that a COVID-19 patient with less than one basic reproduction ratio can automatically recover from the infection.

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