scholarly journals Effect of Vaccination to COVID-19 Disease Progression and Herd Immunity

2021 ◽  
Vol 9 (1) ◽  
pp. 262-272
Author(s):  
Randy L. Caga-anan ◽  
Michelle N. Raza ◽  
Grace Shelda G. Labrador ◽  
Ephrime B. Metillo ◽  
Pierre del Castillo ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Disease Progression ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
The Philippines ◽  
Model Parameters ◽  
Delay Term ◽  
Induced Immunity ◽  
Determining Factor ◽  
Disease Free

Abstract A mathematical model of COVID-19 with a delay-term for the vaccinated compartment is developed. It has parameters accounting for vaccine-induced immunity delay, vaccine effectiveness, vaccination rate, and vaccine-induced immunity duration. The model parameters before vaccination are calibrated with the Philippines’ confirmed cases. Simulations show that vaccination has a significant effect in reducing future infections, with the vaccination rate being the dominant determining factor of the level of reduction. Moreover, depending on the vaccination rate and the vaccine-induced immunity duration, the system could reach a disease-free state but could not attain herd immunity. Simulations are also done to compare the effects of the various available vaccines. Results show that Pfizer-BioNTech has the most promising effect while Sinovac has the worst result relative to the others.

scholarly journals Modeling The Impact of Vaccination On COVID-19 And Its Delta Variant

2021 ◽  
Author(s):  
Jianbo Wang ◽  
Yin-Chi Chan ◽  
Ruiwu Niu ◽  
Eric W. M. Wong ◽  
Michaël Antonie Van Wyk
Keyword(s):  
Hong Kong ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
Hospitalization Rate ◽  
Model Parameters ◽  
Cumulative Number ◽  
Reproduction Numbers ◽  
Important Means ◽  
Model Initialization ◽  
The Impact

Abstract Vaccination is an important means to fight against the spread of the SARS-CoV-2 virus and its variants. In this work, we propose a general susceptible-vaccinated-exposed-infected-hospitalized-removed (SVEIHR) model and derive its basic and effective reproduction numbers. We set Hong Kong as an example to prove the validity of our model. The model shows how the number of confirmed COVID-19 cases in Hong Kong during the second and third waves of the COVID-19 pandemic would have been reduced had vaccination been available then. We then investigate the relationships between various model parameters and the cumulative number of hospitalized COVID-19 cases in Hong Kong for the ancestral and Delta strains of the virus. Next, we compare the evolution of the SVEIHR model to the traditional “herd immunity” threshold where the proportion of vaccinated individuals is static and no further vaccination takes place after model initialization. Numerical results for Hong Kong demonstrate that the static herd immunity threshold corresponds to a cumulative hospitalization ratio of about one percent (assuming the current hospitalization rate of infected individuals is maintained). We also demonstrate that when the vaccination rate is high, the initial proportion of vaccinated individuals can be lowered for while still maintaining the same proportion of cumulative hospitalized individuals.

scholarly journals Covid-19 disease dynamics with vaccination: The effect of uncertainty

2022 ◽  
Author(s):  
Nandadulal Bairagi ◽  
Abhijiit Majumder
Keyword(s):  
Mathematical Models ◽  
Vaccine Efficacy ◽  
Loss Rate ◽  
Vaccination Rate ◽  
Model Parameters ◽  
Extinction Time ◽  
Disease Eradication ◽  
Average Value ◽  
Force Of Infection ◽  
Induced Immunity

Rate parameters are critical in estimating the covid burden using mathematical models. In the Covid-19 mathematical models, these parameters are assumed to be constant. However, uncertainties in these rate parameters are almost inevitable. In this paper, we study a stochastic epidemic model of the SARS-CoV-2 virus infection in the presence of vaccination in which some parameters fluctuate around its average value. Our analysis shows that if the stochastic basic reproduction number (SBRN) of the system is greater than unity, then there is a stationary distribution, implying the long-time disease persistence. A sufficient condition for disease eradication is also prescribed for which the exposed class goes extinct, followed by the infected class. The disease eradication criterion may not hold if the rate of vaccine-induced immunity loss increases or/and the force of infection increases. Using the Indian Covid-19 data, we estimated the model parameters and showed the future disease progression in the presence of vaccination. The disease extinction time is estimated under various conditions. It is revealed that the mean extinction time is an increasing function of both the force of infection and immunity loss rate and shows the lognormal distribution. We point out that disease eradication might not be possible even at a higher vaccination rate if the vaccine-induced immunity loss rate is high. Our observation thus indicates the endemicity of the disease for the existing vaccine efficacy. The disease eradication is possible only with a higher vaccine efficacy or a reduced infection rate.

scholarly journals A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2

Science ◽  
2020 ◽  
Vol 369 (6505) ◽  
pp. 846-849 ◽  
Author(s):  
Tom Britton ◽  
Frank Ball ◽  
Pieter Trapman
Keyword(s):  
Mathematical Model ◽  
Severe Acute Respiratory Syndrome ◽  
Preventive Measures ◽  
Social Activity ◽  
Herd Immunity ◽  
Population Heterogeneity ◽  
Contact Rates ◽  
Mixing Rates ◽  
Age Structured ◽  
Induced Immunity

Despite various levels of preventive measures, in 2020, many countries have suffered severely from the coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Using a model, we show that population heterogeneity can affect disease-induced immunity considerably because the proportion of infected individuals in groups with the highest contact rates is greater than that in groups with low contact rates. We estimate that if R0 = 2.5 in an age-structured community with mixing rates fitted to social activity, then the disease-induced herd immunity level can be ~43%, which is substantially less than the classical herd immunity level of 60% obtained through homogeneous immunization of the population. Our estimates should be interpreted as an illustration of how population heterogeneity affects herd immunity rather than as an exact value or even a best estimate.

scholarly journals Dynamics of A Multi-stage Epidemic Model with and without Treatment

2020 ◽  
Vol 8 (5) ◽  
pp. 5293-5300
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Dynamical Behaviour ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, a non-linear mathematical model is proposed with the thought of treatment to depict the spread of infectious illness and assessed with three contamination stages. We talk about the dynamical behaviour and analytical study of the framework for the mathematical model which shows that it has two non-negative equilibrium points i.e., disease-free equilibrium (DFE) and interior(endemic) equilibrium. The outcomes show that the dynamical behaviour of the model is totally determined by the basic reproduction number. For the basic reproduction number , the disease-free equilibrium is locally as well as globally asymptotically stable under a particular parameter set. In case , the model at the interior equilibrium is locally as well as globally asymptotically stable. Finally, numerical solutions of the model corroborate the analytical results and facilitate a sensitivity analysis of the model parameters.

scholarly journals Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Ashenafi Kelemu Mengistu ◽  
Peter J. Witbooi
Keyword(s):  
Mathematical Model ◽  
High Risk ◽  
Positive Influence ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Incidence Data ◽  
Tuberculosis Transmission ◽  
Sensitivity Indices ◽  
The Stability ◽  
Disease Free

In this study, we develop and analyze a deterministic mathematical model for tuberculosis (TB) transmission dynamics. The model includes vaccination for newborns and treatment for both high-risk latent and active TB patients. The stability of disease-free equilibrium point is discussed in detail. In the numerical simulation, the model parameters are estimated using reported TB incidence data in Ethiopia from the years 2003 to 2017, and R0 is calculated as R0≈2.13. Finally, the sensitivity indices of R0 with respect to the model parameters are performed, and their corresponding graphical results are presented. Our results quantify the positive influence of vaccination and the treatment for high-risk latent and active TB patients on the control of tuberculosis.

scholarly journals High endemic levels of typhoid fever in rural areas of Ghana may stem from optimal voluntary vaccination behaviour

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200354 ◽  
Author(s):  
Carmen B. Acosta-Alonzo ◽  
Igor V. Erovenko ◽  
Aaleah Lancaster ◽  
Hyunju Oh ◽  
Jan Rychtář ◽  
...  
Keyword(s):  
Typhoid Fever ◽  
Rural Areas ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
Epidemiological Model ◽  
Model Parameters ◽  
Theoretic Model ◽  
Vaccination Rates ◽  
Incidence Data ◽  
Optimal Population

Typhoid fever has long established itself endemically in rural Ghana despite the availability of cheap and effective vaccines. We used a game-theoretic model to investigate whether the low vaccination coverage in Ghana could be attributed to rational human behaviour. We adopted a version of an epidemiological model of typhoid fever dynamics, which accounted not only for chronic life-long carriers but also for a short-cycle transmission in the immediate environment and a long-cycle transmission via contamination of the water supply. We calibrated the model parameters based on the known incidence data. We found that unless the (perceived) cost of vaccination is negligible, the individually optimal population vaccination rate falls significantly short of the societally optimal population vaccination rate needed to reach herd immunity. We expressed both the herd immunity and the optimal equilibrium vaccination rates in terms of only a few observable parameters such as the incidence rate, demographics, vaccine waning rate and the perceived cost of vaccination relative to the cost of infection. This allowed us not to rely on other uncertain epidemiological model parameters and, in particular, to bypass uncertainties about the role of the carriers in the transmission.

scholarly journals Dynamics of Toxoplasmosis Disease in Cats population with vaccination

2021 ◽  
pp. 17-25
Author(s):  
Idris Babaji Muhammad ◽  
Salisu Usaini
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Simulations ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Vaccination Rate ◽  
Steady States ◽  
Model Parameters ◽  
Threshold Parameter ◽  
Globally Stable ◽  
Disease Free

We extend the deterministic model for the dynamics of toxoplasmosis proposed by Arenas et al. in 2010, by separating vaccinated and recovered classes. The model exhibits two equilibrium points, the disease-free and endemic steady states. These points are both locally and globally stable asymptotically when the threshold parameter Rv is less than and greater than unity, respectively. The sensitivity analysis of the model parameters reveals that the vaccination parameter $\pi$ is more sensitive to changes than any other parameter. Indeed, as expected the numerical simulations reveal that the higher the vaccination rate of susceptible individuals the smaller the value of the threshold Rv (i.e., increase in $\pi$ results in the decrease in Rv , leading to the eradication of toxoplasmosis in cats population.

scholarly journals Modelling the impact of delaying vaccination against SARS-CoV-2 assuming unlimited vaccine supply

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Marcos Amaku ◽  
Dimas Tadeu Covas ◽  
Francisco Antonio Bezerra Coutinho ◽  
Raymundo Soares Azevedo ◽  
Eduardo Massad
Keyword(s):  
Mathematical Model ◽  
Vaccination Campaign ◽  
Vaccination Rate ◽  
Sao Paulo ◽  
The State ◽  
São Paulo ◽  
Health Authorities ◽  
The World ◽  
The Moment ◽  
The Impact

Abstract Background At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far. Methods We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations. Results The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole. Conclusions Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

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