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21 pages, 10613 KiB

Open AccessArticle

Post-Vaccination and Post-Infection Immunity to the Hepatitis B Virus and Circulation of Immune-Escape Variants in the Russian Federation 20 Years after the Start of Mass Vaccination

by Fedor A. Asadi Mobarkhan, Victor A. Manuylov, Anastasia A. Karlsen, Vera S. Kichatova, Ilya A. Potemkin, Maria A. Lopatukhina, Olga V. Isaeva, Eugeniy V. Mullin, Elena P. Mazunina, Evgeniia N. Bykonia, Denis A. Kleymenov, Liubov I. Popova, Vladimir A. Gushchin, Artem P. Tkachuk, Anna A. Saryglar, Irina E. Kravchenko, Snezhana S. Sleptsova, Victor V. Romanenko, Anna V. Kuznetsova, Sergey A. Solonin, Tatyana A. Semenenko, Mikhail I. Mikhailov and Karen K. Kyuregyan Show full author list Hide full author list

Vaccines 2023, 11(2), 430; https://doi.org/10.3390/vaccines11020430 - 13 Feb 2023

Cited by 1 | Viewed by 1622

Abstract

A neonatal vaccination against the Hepatitis B virus (HBV) infection was initiated in Russia 20 years ago, with catch-up immunization for adolescents and adults under the age of 60 years launched in 2006. Here, we have assessed the humoral immunity to HBV in [...] Read more.

A neonatal vaccination against the Hepatitis B virus (HBV) infection was initiated in Russia 20 years ago, with catch-up immunization for adolescents and adults under the age of 60 years launched in 2006. Here, we have assessed the humoral immunity to HBV in different regions of Russia, as well as the infection frequency following 20 years of a nationwide vaccination campaign. We have also evaluated the role of immune-escape variants in continuing HBV circulation. A total of 36,149 healthy volunteers from nine regions spanning the Russian Federation from west to east were tested for HBV surface antigen (HBsAg), antibodies to HBV capsid protein (anti-HBc), and antibodies to HBsAg (anti-HBs). HBV sequences from 481 chronic Hepatitis B patients collected from 2018–2022 were analyzed for HBsAg immune-escape variants, compared with 205 sequences obtained prior to 2010. Overall, the HBsAg detection rate was 0.8%, with this level significantly exceeded only in one study region, the Republic of Dagestan (2.4%, p < 0.0001). Among the generation vaccinated at birth, the average HBsAg detection rate was below 0.3%, ranging from 0% to 0.7% depending on the region. The anti-HBc detection rate in subjects under 20 years was 7.4%, indicating ongoing HBV circulation. The overall proportion of participants under 20 years with vaccine-induced HBV immunity (anti-HBs positive, anti-HBc negative) was 41.7% but below 10% in the Tuva Republic and below 25% in the Sverdlovsk and Kaliningrad regions. The overall prevalence of immune-escape HBsAg variants was 25.2% in sequences obtained from 2018–2022, similar to the prevalence of 25.8% in sequences collected prior to 2010 (p > 0.05). The population dynamics of immune-escape variants predicted by Bayesian analysis have remained stable over the last 20 years, indicating the absence of vaccine-driven positive selection. In contrast, the wild-type HBV population size experienced a rapid decrease starting in the mid-1990s, following the introduction of mass immunization, but it subsequently began to recover, reaching pre-vaccination levels by 2020. Taken together, these data indicate that it is gaps in vaccination, and not virus evolution, that may be responsible for the continued virus circulation despite 20 years of mass vaccination. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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17 pages, 1394 KiB

Open AccessArticle

Mathematical Modeling and Analysis of the Dynamics of RNA Viruses in Presence of Immunity and Treatment: A Case Study of SARS-CoV-2

by Khalid Hattaf, Mly Ismail El Karimi, Ahmed A. Mohsen, Zakaria Hajhouji, Majda El Younoussi and Noura Yousfi

Vaccines 2023, 11(2), 201; https://doi.org/10.3390/vaccines11020201 - 17 Jan 2023

Cited by 12 | Viewed by 1702

Abstract

The emergence of novel RNA viruses like SARS-CoV-2 poses a greater threat to human health. Thus, the main objective of this article is to develop a new mathematical model with a view to better understand the evolutionary behavior of such viruses inside the [...] Read more.

The emergence of novel RNA viruses like SARS-CoV-2 poses a greater threat to human health. Thus, the main objective of this article is to develop a new mathematical model with a view to better understand the evolutionary behavior of such viruses inside the human body and to determine control strategies to deal with this type of threat. The developed model takes into account two modes of transmission and both classes of infected cells that are latently infected cells and actively infected cells that produce virus particles. The cure of infected cells in latent period as well as the lytic and non-lytic immune response are considered into the model. We first show that the developed model is well-posed from the biological point of view by proving the non-negativity and boundedness of model’s solutions. Our analytical results show that the dynamical behavior of the model is fully determined by two threshold parameters one for viral infection and the other for humoral immunity. The effect of antiviral treatment is also investigated. Furthermore, numerical simulations are presented in order to illustrate our analytical results. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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22 pages, 1691 KiB

Open AccessArticle

A Mathematical Model of Vaccinations Using New Fractional Order Derivative

by Asma, Mehreen Yousaf, Muhammad Afzaal, Mahmoud H. DarAssi, Muhammad Altaf Khan, Mohammad Y. Alshahrani and Muath Suliman

Vaccines 2022, 10(12), 1980; https://doi.org/10.3390/vaccines10121980 - 22 Nov 2022

Cited by 6 | Viewed by 1777

Abstract

Purpose: This paper studies a simple SVIR (susceptible, vaccinated, infected, recovered) type of model to investigate the coronavirus’s dynamics in Saudi Arabia with the recent cases of the coronavirus. Our purpose is to investigate coronavirus cases in Saudi Arabia and to predict the [...] Read more.

Purpose: This paper studies a simple SVIR (susceptible, vaccinated, infected, recovered) type of model to investigate the coronavirus’s dynamics in Saudi Arabia with the recent cases of the coronavirus. Our purpose is to investigate coronavirus cases in Saudi Arabia and to predict the early eliminations as well as future case predictions. The impact of vaccinations on COVID-19 is also analyzed. Methods: We consider the recently introduced fractional derivative known as the generalized Hattaf fractional derivative to extend our COVID-19 model. To obtain the fitted and estimated values of the parameters, we consider the nonlinear least square fitting method. We present the numerical scheme using the newly introduced fractional operator for the graphical solution of the generalized fractional differential equation in the sense of the Hattaf fractional derivative. Mathematical as well as numerical aspects of the model are investigated. Results: The local stability of the model at disease-free equilibrium is shown. Further, we consider real cases from Saudi Arabia since 1 May–4 August 2022, to parameterize the model and obtain the basic reproduction number

R_{0}^{v} \approx 2.92

. Further, we find the equilibrium point of the endemic state and observe the possibility of the backward bifurcation for the model and present their results. We present the global stability of the model at the endemic case, which we found to be globally asymptotically stable when

R_{0}^{v} > 1

. Conclusion: The simulation results using the recently introduced scheme are obtained and discussed in detail. We present graphical results with different fractional orders and found that when the order is decreased, the number of cases decreases. The sensitive parameters indicate that future infected cases decrease faster if face masks, social distancing, vaccination, etc., are effective. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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23 pages, 610 KiB

Open AccessArticle

Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy

by Amar Nath Chatterjee, Fahad Al Basir, Dibyendu Biswas and Teklebirhan Abraha

Vaccines 2022, 10(11), 1846; https://doi.org/10.3390/vaccines10111846 - 31 Oct 2022

Cited by 2 | Viewed by 1268

Abstract

Mathematical modeling is crucial to investigating tthe ongoing coronavirus disease 2019 (COVID-19) pandemic. The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower respiratory tract. During this viral infection, infected cells can activate innate and adaptive immune responses [...] Read more.

Mathematical modeling is crucial to investigating tthe ongoing coronavirus disease 2019 (COVID-19) pandemic. The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower respiratory tract. During this viral infection, infected cells can activate innate and adaptive immune responses to viral infection. Immune response in COVID-19 infection can lead to longer recovery time and more severe secondary complications. We formulate a micro-level mathematical model by incorporating a saturation term for SARS-CoV-2-infected epithelial cell loss reliant on infected cell levels. Forward and backward bifurcation between disease-free and endemic equilibrium points have been analyzed. Global stability of both disease-free and endemic equilibrium is provided. We have seen that the disease-free equilibrium is globally stable for

R_{0} < 1

, and endemic equilibrium exists and is globally stable for

R_{0} > 1

. Impulsive application of drug dosing has been applied for the treatment of COVID-19 patients. Additionally, the dynamics of the impulsive system are discussed when a patient takes drug holidays. Numerical simulations support the analytical findings and the dynamical regimes in the systems. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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25 pages, 809 KiB

Open AccessArticle

Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown

by Dawit Denu and Seth Kermausuor

Vaccines 2022, 10(11), 1773; https://doi.org/10.3390/vaccines10111773 - 22 Oct 2022

Cited by 6 | Viewed by 1279

Abstract

The outbreak of the coronavirus disease (COVID-19) has caused a lot of disruptions around the world. In an attempt to control the spread of the disease among the population, several measures such as lockdown, and mask mandates, amongst others, were implemented by many [...] Read more.

The outbreak of the coronavirus disease (COVID-19) has caused a lot of disruptions around the world. In an attempt to control the spread of the disease among the population, several measures such as lockdown, and mask mandates, amongst others, were implemented by many governments in their countries. To understand the effectiveness of these measures in controlling the disease, several mathematical models have been proposed in the literature. In this paper, we study a mathematical model of the coronavirus disease with lockdown by employing the Caputo fractional-order derivative. We establish the existence and uniqueness of the solution to the model. We also study the local and global stability of the disease-free equilibrium and endemic equilibrium solutions. By using the residual power series method, we obtain a fractional power series approximation of the analytic solution. Finally, to show the accuracy of the theoretical results, we provide some numerical and graphical results. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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17 pages, 713 KiB

Open AccessArticle

A New Stochastic Split-Step θ-Nonstandard Finite Difference Method for the Developed SVIR Epidemic Model with Temporary Immunities and General Incidence Rates

by Abdulwasea Alkhazzan, Jungang Wang, Yufeng Nie and Khalid Hattaf

Vaccines 2022, 10(10), 1682; https://doi.org/10.3390/vaccines10101682 - 09 Oct 2022

Cited by 6 | Viewed by 1254

Abstract

In this paper, an SVIR epidemic model with temporary immunities and general incidence rates is constructed and analyzed. By utilizing Lyapunov functions, we prove the existence and uniqueness of the positive global solution of the constructed model, as well as the sufficient conditions [...] Read more.

In this paper, an SVIR epidemic model with temporary immunities and general incidence rates is constructed and analyzed. By utilizing Lyapunov functions, we prove the existence and uniqueness of the positive global solution of the constructed model, as well as the sufficient conditions of extinction and persistence of disease, are provided. Due to the difficulty of obtaining the analytical solution to our model, we construct two numerical schemes to generate an approximate solution to the model. The first one is called the split-step

θ

-Milstein (SSTM) method, and the second one is called the stochastic split-step

θ

-nonstandard finite difference (SSSNSFD) method, which is designed by merging split-step

θ

method with stochastic nonstandard finite difference method for the first time in this paper. Further, we prove the positivity, boundedness, and stability of the SSSTNSFD method. By employing the two mentioned methods, we support the validity of the studied theoretical results, as well, the effect of the length of immunity periods, parameters values of the incidence rates, and noise on the dynamics of the model are discussed and simulated. The increase in the size of time step size plays a vital role in revealing the method that preserves positivity, boundedness, and stability. To this end, a comparison between the proposed numerical methods is carried out graphically. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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14 pages, 2379 KiB

Open AccessArticle

Dynamic Changes in Hepatitis A Immunity in Regions with Different Vaccination Strategies and Different Vaccination Coverage

by Karen K. Kyuregyan, Maria A. Lopatukhina, Fedor A. Asadi Mobarkhan, Vera S. Kichatova, Ilya A. Potemkin, Olga V. Isaeva, Anastasia A. Karlsen, Elena Yu. Malinnikova, Alla N. Kaira, Tatyana V. Kozhanova, Victor A. Manuylov, Elena P. Mazunina, Evgeniia N. Bykonia, Denis A. Kleymenov, Margarita E. Ignateva, Olga E. Trotsenko, Anna V. Kuznetsova, Anna A. Saryglar, Natalia D. Oorzhak, Victor V. Romanenko and Mikhail I. Mikhailov Show full author list Hide full author list

Vaccines 2022, 10(9), 1423; https://doi.org/10.3390/vaccines10091423 - 29 Aug 2022

Cited by 2 | Viewed by 1857

Abstract

The data on hepatitis A virus (HAV) seroprevalence are critical for the implementation of a universal mass vaccination (UMV) strategy. The latter has not been implemented in Russia; however, regional child vaccination programs have been adopted in some parts of the country. The [...] Read more.

The data on hepatitis A virus (HAV) seroprevalence are critical for the implementation of a universal mass vaccination (UMV) strategy. The latter has not been implemented in Russia; however, regional child vaccination programs have been adopted in some parts of the country. The aim of this study is to assess changes in HAV immunity within the last decade in regions of Russia with different vaccination strategies and different vaccination coverage rates. In regions where UMV has not been implemented and HAV vaccination coverage rates do not exceed the national average, the 50% seroprevalence threshold has shifted in the Moscow region from people aged under 40 years in 2008 to people aged over 59 years in 2020, and from people aged under 30 years to people aged over 40 years in the Khabarovsk region. In two regions (Yakutia and Sverdlovsk), a two-dose-based UMV scheme has been in place since 2011 and 2003, respectively, and in Tuva single-dose child immunization was launched in 2012. These regional programs have resulted in a significant increase in HAV seroprevalence in children and adolescents. In Yakutia, 50% herd immunity had been achieved by 2020 in age groups under 20 years, compared to 20–30% seroprevalence rates in 2008. In the Sverdlovsk region, HAV immunity has increased to >65% over the decade in children aged over 10 years, adolescents and young adults, whereas it declined in older age groups. However, a three-fold drop in HAV immunity has occurred in children under 10 years of age, reflecting a significant decline in vaccination coverage. In Tuva, HAV immunity rates in children under 10 years old increased two-fold to exceed 50% by 2020. These data suggest that UMV should be implemented on a national level. Measures to control vaccination coverage and catch-up vaccination campaigns are recommended in order to maintain the effectiveness of existing HAV vaccination programs. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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29 pages, 2592 KiB

Open AccessArticle

An Optimal Control Model to Understand the Potential Impact of the New Vaccine and Transmission-Blocking Drugs for Malaria: A Case Study in Papua and West Papua, Indonesia

by Bevina D. Handari, Rossi A. Ramadhani, Chidozie W. Chukwu, Sarbaz H. A. Khoshnaw and Dipo Aldila

Vaccines 2022, 10(8), 1174; https://doi.org/10.3390/vaccines10081174 - 24 Jul 2022

Cited by 9 | Viewed by 2244

Abstract

Malaria is one of the major causes of a high death rate due to infectious diseases every year. Despite attempts to eradicate the disease, results have not been very successful. New vaccines and other treatments are being constantly developed to seek optimal ways [...] Read more.

Malaria is one of the major causes of a high death rate due to infectious diseases every year. Despite attempts to eradicate the disease, results have not been very successful. New vaccines and other treatments are being constantly developed to seek optimal ways to prevent malaria outbreaks. In this article, we formulate and analyze an optimal control model of malaria incorporating the new pre-erythrocytic vaccine and transmission-blocking treatment. Sufficient conditions to guarantee local stability of the malaria-free equilibrium were derived based on the controlled reproduction number condition. Using the non-linear least square fitting method, we fitted the incidence data from the province of Papua and West Papua in Indonesia to estimate the model parameter values. The optimal control characterization and optimality conditions were derived by applying the Pontryagin Maximum Principle, and numerical simulations were also presented. Simulation results show that both the pre-erythrocytic vaccine and transmission-blocking treatment significantly reduce the spread of malaria. Accordingly, a high doses of pre-erythrocytic vaccine is needed if the number of infected individuals is relatively small, while transmission blocking is required if the number of infected individuals is relatively large. These results suggest that a large-scale implementation of both strategies is vital as the world continues with the effort to eradicate malaria, especially in endemic regions across the globe. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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20 pages, 781 KiB

Open AccessArticle

Competition of SARS-CoV-2 Variants in Cell Culture and Tissue: Wins the Fastest Viral Autowave

by Alexey Tokarev, Anastasia Mozokhina and Vitaly Volpert

Vaccines 2022, 10(7), 995; https://doi.org/10.3390/vaccines10070995 - 22 Jun 2022

Cited by 3 | Viewed by 1398

Abstract

Replication of viruses in living tissues and cell cultures is a “number game” involving complex biological processes (cell infection, virus replication inside infected cell, cell death, viral degradation) as well as transport processes limiting virus spatial propagation. In epithelial tissues and immovable cell [...] Read more.

Replication of viruses in living tissues and cell cultures is a “number game” involving complex biological processes (cell infection, virus replication inside infected cell, cell death, viral degradation) as well as transport processes limiting virus spatial propagation. In epithelial tissues and immovable cell cultures, viral particles are basically transported via Brownian diffusion. Highly non-linear kinetics of viral replication combined with diffusion limitation lead to spatial propagation of infection as a moving front switching from zero to high local viral concentration, the behavior typical of spatially distributed excitable media. We propose a mathematical model of viral infection propagation in cell cultures and tissues under the diffusion limitation. The model is based on the reaction–diffusion equations describing the concentration of uninfected cells, exposed cells (infected but still not shedding the virus), virus-shedding cells, and free virus. We obtain the expressions for the viral replication number, which determines the condition for spatial infection progression, and for the final concentration of uninfected cells. We determine analytically the speed of spatial infection propagation and validate it numerically. We calibrate the model to recent experimental data on SARS-CoV-2 Delta and Omicron variant replication in human nasal epithelial cells. In the case of competition of two virus variants in the same cell culture, the variant with larger individual spreading speed wins the competition and eliminates another one. These results give new insights concerning the emergence of new variants and their spread in the population. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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22 pages, 1947 KiB

Open AccessArticle

A Modeling Study on Vaccination and Spread of SARS-CoV-2 Variants in Italy

by Chiara Antonini, Sara Calandrini and Fortunato Bianconi

Vaccines 2021, 9(8), 915; https://doi.org/10.3390/vaccines9080915 - 17 Aug 2021

Cited by 8 | Viewed by 2970

Abstract

From the end of 2020, different vaccines against COVID-19 have been approved, offering a glimmer of hope and relief worldwide. However, in late 2020, new cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) started to re-surge, worsened by the emergence of highly [...] Read more.

From the end of 2020, different vaccines against COVID-19 have been approved, offering a glimmer of hope and relief worldwide. However, in late 2020, new cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) started to re-surge, worsened by the emergence of highly infectious variants. To study this scenario, we extend the Susceptible-Exposed-Infectious-Removed model with lockdown measures used in our previous work with the inclusion of new lineages and mass vaccination campaign. We estimate model parameters using the Bayesian method Conditional Robust Calibration in two case studies: Italy and the Umbria region, the Italian region being worse affected by the emergence of variants. We then use the model to explore the dynamics of COVID-19, given different vaccination paces and a policy of gradual reopening. Our findings confirm the higher reproduction number of Umbria and the increase of transmission parameters due to the presence of new variants. The results illustrate the importance of preserving population-wide interventions, especially during the beginning of vaccination. Finally, under the hypothesis of waning immunity, the predictions show that a seasonal vaccination with a constant rate would probably be necessary to control the epidemic. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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26 pages, 1039 KiB

Open AccessArticle

Agent Based Model of Anti-Vaccination Movements: Simulations and Comparison with Empirical Data

by Pawel Sobkowicz and Antoni Sobkowicz

Vaccines 2021, 9(8), 809; https://doi.org/10.3390/vaccines9080809 - 21 Jul 2021

Cited by 9 | Viewed by 4736

Abstract

Background: A realistic description of the social processes leading to the increasing reluctance to various forms of vaccination is a very challenging task. This is due to the complexity of the psychological and social mechanisms determining the positioning of individuals and groups [...] Read more.

Background: A realistic description of the social processes leading to the increasing reluctance to various forms of vaccination is a very challenging task. This is due to the complexity of the psychological and social mechanisms determining the positioning of individuals and groups against vaccination and associated activities. Understanding the role played by social media and the Internet in the current spread of the anti-vaccination (AV) movement is of crucial importance. Methods: We present novel, long-term Big Data analyses of Internet activity connected with the AV movement for such different societies as the US and Poland. The datasets we analyzed cover multiyear periods preceding the COVID-19 pandemic, documenting the behavior of vaccine related Internet activity with high temporal resolution. To understand the empirical observations, in particular the mechanism driving the peaks of AV activity, we propose an Agent Based Model (ABM) of the AV movement. The model includes the interplay between multiple driving factors: contacts with medical practitioners and public vaccination campaigns, interpersonal communication, and the influence of the infosphere (social networks, WEB pages, user comments, etc.). The model takes into account the difference between the rational approach of the pro-vaccination information providers and the largely emotional appeal of anti-vaccination propaganda. Results: The datasets studied show the presence of short-lived, high intensity activity peaks, much higher than the low activity background. The peaks are seemingly random in size and time separation. Such behavior strongly suggests a nonlinear nature for the social interactions driving the AV movement instead of the slow, gradual growth typical of linear processes. The ABM simulations reproduce the observed temporal behavior of the AV interest very closely. For a range of parameters, the simulations result in a relatively small fraction of people refusing vaccination, but a slight change in critical parameters (such as willingness to post anti-vaccination information) may lead to a catastrophic breakdown of vaccination support in the model society, due to nonlinear feedback effects. The model allows the effectiveness of strategies combating the anti-vaccination movement to be studied. An increase in intensity of standard pro-vaccination communications by government agencies and medical personnel is found to have little effect. On the other hand, focused campaigns using the Internet and social media and copying the highly emotional and narrative-focused format used by the anti-vaccination activists can diminish the AV influence. Similar effects result from censoring and taking down anti-vaccination communications by social media platforms. The benefit of such tactics might, however, be offset by their social cost, for example, the increased polarization and potential to exploit it for political goals, or increased ‘persecution’ and ‘martyrdom’ tropes. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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26 pages, 3664 KiB

Open AccessArticle

On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible

by Manuel De la Sen, Santiago Alonso-Quesada, Asier Ibeas and Raul Nistal

Vaccines 2021, 9(4), 398; https://doi.org/10.3390/vaccines9040398 - 18 Apr 2021

Cited by 13 | Viewed by 2670

Abstract

A new discrete susceptible-exposed-infectious-recovered (SEIR) epidemic model is presented subject to a feedback vaccination effort involving two doses. Both vaccination doses, which are subject to a non-necessarily identical effectiveness, are administrated by respecting a certain mutual delay interval, and their immunity effect is [...] Read more.

A new discrete susceptible-exposed-infectious-recovered (SEIR) epidemic model is presented subject to a feedback vaccination effort involving two doses. Both vaccination doses, which are subject to a non-necessarily identical effectiveness, are administrated by respecting a certain mutual delay interval, and their immunity effect is registered after a certain delay since the second dose. The delays and the efficacies of the doses are parameters, which can be fixed in the model for each concrete experimentation. The disease-free equilibrium point is characterized as well as its stability properties, while it is seen that no endemic equilibrium point exists. The exposed subpopulation is supposed to be infective eventually, under a distinct transmission rate of that of the infectious subpopulation. Some simulation examples are presented by using disease parameterizations of the COVID-19 pandemic under vaccination efforts requiring two doses. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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Review

Jump to: Research

15 pages, 387 KiB

Open AccessReview

Biothermodynamics of Viruses from Absolute Zero (1950) to Virothermodynamics (2022)

by Marko Popovic

Vaccines 2022, 10(12), 2112; https://doi.org/10.3390/vaccines10122112 - 09 Dec 2022

Cited by 19 | Viewed by 1996

Abstract

Biothermodynamics of viruses is among the youngest but most rapidly developing scientific disciplines. During the COVID-19 pandemic, it closely followed the results published by molecular biologists. Empirical formulas were published for 50 viruses and thermodynamic properties for multiple viruses and virus variants, including [...] Read more.

Biothermodynamics of viruses is among the youngest but most rapidly developing scientific disciplines. During the COVID-19 pandemic, it closely followed the results published by molecular biologists. Empirical formulas were published for 50 viruses and thermodynamic properties for multiple viruses and virus variants, including all variants of concern of SARS-CoV-2, SARS-CoV, MERS-CoV, Ebola virus, Vaccinia and Monkeypox virus. A review of the development of biothermodynamics of viruses during the last several decades and intense development during the last 3 years is described in this paper. Full article

(This article belongs to the Special Issue Dynamic Models in Viral Immunology)

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