scholarly journals Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 386-426
Author(s):  
Reinhard Schlickeiser ◽  
Martin Kröger
Keyword(s):  
Time Evolution ◽  
Vaccination Rate ◽  
Cumulative Number ◽  
Sir Epidemic Model ◽  
Vaccination Rates ◽  
Sir Epidemic ◽  
Daily Rate ◽  
Inverse Solutions ◽  
Vaccination Campaigns ◽  
Lambert Functions

With the vaccination against Covid-19 now available, how vaccination campaigns influence the mathematical modeling of epidemics is quantitatively explored. In this paper, the standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to a fourth compartment, V, of vaccinated persons. This extension involves the time t-dependent effective vaccination rate, v(t), that regulates the relationship between susceptible and vaccinated persons. The rate v(t) competes with the usual infection, a(t), and recovery, μ(t), rates in determining the time evolution of epidemics. The occurrence of a pandemic outburst with rising rates of new infections requires k+b<1−2η, where k=μ(0)/a(0) and b=v(0)/a(0) denote the initial values for the ratios of the three rates, respectively, and η≪1 is the initial fraction of infected persons. Exact analytical inverse solutions t(Q) for all relevant quantities Q=[S,I,R,V] of the resulting SIRV model in terms of Lambert functions are derived for the semi-time case with time-independent ratios k and b between the recovery and vaccination rates to the infection rate, respectively. These inverse solutions can be approximated with high accuracy, yielding the explicit time-dependences Q(t) by inverting the Lambert functions. The values of the three parameters k, b and η completely determine the reduced time evolution of the SIRV-quantities Q(τ). The influence of vaccinations on the total cumulative number and the maximum rate of new infections in different countries is calculated by comparing with monitored real time Covid-19 data. The reduction in the final cumulative fraction of infected persons and in the maximum daily rate of new infections is quantitatively determined by using the actual pandemic parameters in different countries. Moreover, a new criterion is developed that decides on the occurrence of future Covid-19 waves in these countries. Apart from in Israel, this can happen in all countries considered.

scholarly journals Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations

2021 ◽  
Author(s):  
Reinhard Schlickeiser ◽  
Martin Kröger
Keyword(s):  
Time Evolution ◽  
Vaccination Rate ◽  
Cumulative Number ◽  
Sir Epidemic Model ◽  
Vaccination Rates ◽  
Sir Epidemic ◽  
Daily Rate ◽  
Inverse Solutions ◽  
Vaccination Campaigns ◽  
Lambert Functions

With the now available vaccination against Covid-19 it is quantitatively explored how vaccination campaigns influence the mathematical modeling of epidemics. The standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to the fourth compartment V of vaccinated persons and the vaccination rate v(t) that regulates the relation between susceptible and vaccinated persons. The vaccination rate v(t) competes with the infection (a(t)) and recovery (\mu(t)) rates in determining the time evolution of epidemics. In order for a pandemic outburst with rising rates of new infections it is required that k+b&lt;1-2\eta, where k=\mu_0/a_0 and b=v_0/a_0 denote the initial ratios of the three rates, respectively, and \eta &lt;&lt; 1 is the initial fraction of infected persons. Exact analytical inverse solutions t(Q) for all relevant quantities Q=[S,I,R,V] of the resulting SIRV-model in terms of Lambert functions are derived for the semi-time case with time-independent ratios k and b between the recovery and vaccination rates to the infection rate, respectively. These inverse solutions can be approximated with high accuracy yielding the explicit time-dependences Q(t) by inverting the Lambert functions. The values of the three parameters k, b and \eta completely determine the reduced time evolution the SIRV-quantities Q(\tau). The influence of vaccinations on the total cumulative number and the maximum rate of new infections in different countries is calculated by comparing with monitored real time Covid-19 data. The reduction in the final cumulative fraction of infected persons and in the maximum daily rate of new infections is quantitatively determined by using the actual pandemic parameters in different countries. Moreover, a new criterion is developed that decides on the occurrence of future Covid-19 waves in these countries. Apart from Israel this can happen in all countries considered.

scholarly journals Modeling the Effect of Population-Wide Vaccination on the Evolution of COVID-19 Epidemic in Canada

2021 ◽  
Author(s):  
Intissar Harizi ◽  
Soulaimane Berkane ◽  
Abdelhamid Tayebi
Keyword(s):  
Vaccine Efficacy ◽  
Vaccination Campaign ◽  
Vaccination Rate ◽  
Prevention Measures ◽  
Vaccination Rates ◽  
Daily Rate ◽  
The World ◽  
Additional State ◽  
Vaccination Campaigns

AbstractPopulation-wide vaccination is critical for containing the COVID-19 pandemic when combined with effective testing and prevention measures. Since the beginning of the COVID-19 outbreak, several companies worked tirelessly for the development of an efficient vaccine that would put an end to this pandemic. Today, a number of COVID-19 vaccines have been approved for use by a number of national regulatory organizations. Vaccination campaigns have already started in several countries with different daily-vaccination rates depending on the country’s vaccination capacity. Therefore, we find it timely and extremely important to conduct a study on the effect of population-wide vaccination campaigns on the evolution of the COVID-19 epidemic. To this end, we propose a new deterministic mathematical model to forecast the COVID-19 epidemic evolution under the effect of vaccination and vaccine efficacy. This model, referred to as SIRV, consists of a compartmental SIR (susceptible, infectious and removed) model augmented with an additional state V representing the effectively vaccinated population as well as two inputs representing the daily-vaccination rate and the vaccine efficacy. Using our SIRV model, we predict the evolution of the COVID-19 epidemic in Canada and its most affected provinces (Ontario, Quebec, British Columbia, Alberta, Saskatchewan, and Manitoba), for different daily vaccination rates and vaccine efficacy. Projections suggest that, without vaccination, 219, 000 lives could be lost across Canada by the end of 2021 due to COVID-19. The ongoing vaccination campaign across Canada seems to unfold relatively slowly at an average daily rate close to 1/2 vaccine per 1, 000 population. At this pace, we could be saving more than 77, 496 lives by the end of the year. Doubling the current vaccination efforts (1 vaccine per day per 1, 000 population) could be sufficient to save 125, 839 lives in Canada during the current year 2021. We would like to point out that our study assumes that the vaccine is perfectly safe without any short or long term side-effects. This study has been conducted independently at arm’s length from vaccine manufacturers, using the available data from Canada health services. This study can be easily adapted to other places in the world.

scholarly journals Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Shujing Gao ◽  
Zhidong Teng ◽  
Juan J. Nieto ◽  
Angela Torres
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Epidemic Model ◽  
Discrete Dynamical System ◽  
Vaccination Rate ◽  
Sir Epidemic Model ◽  
Pulse Vaccination ◽  
Sir Epidemic ◽  
Distributed Time Delay ◽  
Large Pulse

Pulse vaccination, the repeated application of vaccine over a defined age range, is gaining prominence as an effective strategy for the elimination of infectious diseases. An SIR epidemic model with pulse vaccination and distributed time delay is proposed in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than some critical value. The permanence of the model is investigated analytically. Our results indicate that a large pulse vaccination rate is sufficient for the eradication of the disease.

scholarly journals The importance of sustained compliance with physical distancing during COVID-19 vaccination rollout

2021 ◽  
Author(s):  
Alexandra Teslya ◽  
Ganna Rozhnova ◽  
Thi Mui Pham ◽  
Daphne van Wees ◽  
Hendrik Nunner ◽  
...  
Keyword(s):  
Vaccination Coverage ◽  
Vaccine Coverage ◽  
Transmission Model ◽  
Cumulative Number ◽  
Vaccination Rates ◽  
Contact Rates ◽  
Health Authorities ◽  
Public Health Authorities ◽  
Vaccination Campaigns ◽  
The Impact

Abstract Mass vaccination campaigns against SARS-CoV-2 are under way in many countries with the hope that increasing vaccination coverage will enable reducing current physical distancing measures. Compliance with these measures is waning, while more transmissible virus variants such as B.1.1.7 have emerged. Using SARS-CoV-2 transmission model we investigated the impact of the feedback between compliance, the incidence of infection, and vaccination coverage on the success of a vaccination programme in the population where waning of compliance depends on vaccine coverage. Our results suggest that the combination of fast waning compliance, slow vaccination rates, and more transmissible variants may result in a higher cumulative number of infections than in a situation without vaccination. These adverse effects can be alleviated if vaccinated individuals do not revert to pre-pandemic contact rates, and if non-vaccinated individuals remain compliant with physical distancing measures. Both require convincing, clear and appropriately targeted communication strategies by public health authorities.

scholarly journals Insecurity, polio vaccination rates, and polio incidence in northwest Pakistan

2018 ◽  
Vol 115 (7) ◽  
pp. 1593-1598 ◽  
Author(s):  
Amol A. Verma ◽  
Marcia P. Jimenez ◽  
Rudolf H. Tangermann ◽  
S. V. Subramanian ◽  
Fahad Razak
Keyword(s):  
Fixed Effects ◽  
Polio Eradication ◽  
Vaccination Rate ◽  
Vaccination Rates ◽  
Number Of Children ◽  
Routinely Collected Health Data ◽  
Polio Vaccination ◽  
Vaccination Campaigns ◽  
Endemic Transmission ◽  
Security Incidents

Pakistan is one of three countries in which endemic transmission of poliovirus has never been stopped. Insecurity is often cited but poorly studied as a barrier to eradicating polio. We analyzed routinely collected health data from 32 districts of northwest Pakistan and constructed an index of insecurity based on journalistic reports of the monthly number of deaths and injuries resulting from conflict-related security incidents. The primary outcomes were the monthly incidence of paralytic polio cases within each district between 2007 and 2014 and the polio vaccination percentage from 666 district-level vaccination campaigns between 2007 and 2009, targeting ∼5.7 million children. Multilevel Poisson regression controlling for time and district fixed effects was used to model the association between insecurity, vaccinator access, vaccination rates, and polio incidence. The number of children inaccessible to vaccinators was 19.7% greater (95% CI: 19.2–20.2%), and vaccination rates were 5.3% lower (95% CI: 5.2–5.3%) in “high-insecurity” campaigns compared with “secure” campaigns. The unadjusted mean vaccination rate was 96.3% (SD = 8.6) in secure campaigns and 88.3% (SD = 19.2) in high-insecurity campaigns. Polio incidence was 73.0% greater (95% CI: 30–131%) during high-insecurity months (unadjusted mean = 0.13 cases per million people, SD = 0.71) compared with secure months (unadjusted mean = 1.23 cases per million people, SD = 4.28). Thus, insecurity was associated with reduced vaccinator access, reduced polio vaccination, and increased polio incidence in northwest Pakistan. These findings demonstrate that insecurity is an important obstacle to global polio eradication.

scholarly journals Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yongzhen Pei ◽  
Li Changguo ◽  
Qianyong Wu ◽  
Yunfei Lv
Keyword(s):  
Dynamic Behavior ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccination Rate ◽  
Disease Spread ◽  
Computational Techniques ◽  
Threshold Condition ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
The Basic Reproduction Number

A delay SIR epidemic model with difference in immunity and successive vaccination is proposed to understand their effects on the disease spread. From theorems, it is obtained that the basic reproduction number governs the dynamic behavior of the system. The existence and stability of the possible equilibria are examined in terms of a certain threshold condition about the basic reproduction number. By use of new computational techniques for delay differential equations, we prove that the system is permanent. Our results indicate that the recovery rate and the vaccination rate are two factors for the dynamic behavior of the system. Numerical simulations are carried out to investigate the influence of the key parameters on the spread of the disease, to support the analytical conclusion, and to illustrate possible behavioral scenarios of the model.

scholarly journals Flu and Pneumococcal Vaccine Coverage in Scleroderma Patients Still Need to Be Prompted: A Systematic Review

Vaccines ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1330
Author(s):  
Francesca Rosamilia ◽  
Giovanni Noberasco ◽  
Dario Olobardi ◽  
Andrea Orsi ◽  
Giancarlo Icardi ◽  
...  
Keyword(s):  
Systematic Review ◽  
Vaccine Coverage ◽  
Pneumococcal Vaccination ◽  
Vaccination Rate ◽  
Vaccination Rates ◽  
Increased Risk ◽  
Flu Vaccine ◽  
Vaccination Campaigns ◽  
Low Coverage ◽  
Current Guidelines

Systemic sclerosis (scleroderma, SSc) is an autoimmune connective tissue disease characterized by excessive production of collagen and multiorgan involvement. Scleroderma patients are at increased risk of influenza complications and pneumonia; thus, vaccinations are recommended. This systematic review evaluated the influenza and pneumococcus vaccination coverage for SSc patients. We included all studies from Pubmed reporting on influenza and pneumococcal vaccination rate in Scleroderma patients up to May 2021. The 14 studies thus selected identified a suboptimal vaccination rate in autoimmune and SSc patients, ranging from 28 to 59% for the flu vaccine, and from 11 to 58% for the pneumo vaccine in absence of specific vaccination campaigns, variously considering also other variables such as age, gender, vaccination settings, and possible vaccination campaigns. We also considered the reasons for low coverage and the approaches that might increase the vaccination rates. A lack of knowledge about the importance of vaccination in these patients and their doctors underlined the need to increase the awareness for vaccination in this patients’ category. Current guidelines recommend vaccination in elderly people and people affected by particular conditions that widely overlap with SSc, yet autoimmune diseases are not always clearly mentioned. Improving this suboptimal vaccination rate with clear guidelines is crucial for SSc patients and for clinicians to immunize these categories based principally on the pathology, prior to the age. Recommendations by the immunologist and the direct link to the vaccine providers can highly improve the vaccine coverage.

scholarly journals The importance of sustained compliance with physical distancing during COVID-19 vaccination rollout

2021 ◽  
Author(s):  
Alexandra Teslya ◽  
Ganna Rozhnova ◽  
Thi Mui Pham ◽  
Daphne van Wees ◽  
Hendrik Nunner ◽  
...  
Keyword(s):  
Vaccination Coverage ◽  
Vaccine Coverage ◽  
Transmission Model ◽  
Cumulative Number ◽  
Vaccination Rates ◽  
Contact Rates ◽  
Health Authorities ◽  
Public Health Authorities ◽  
Vaccination Campaigns ◽  
The Impact

Abstract Mass vaccination campaigns against SARS-CoV-2 are under way in many countries with the hope that increasing vaccination coverage will enable reducing current physical distancing measures. Compliance with these measures is waning, while more transmissible virus variants such as B.1.1.7 have emerged. Using SARS-CoV-2 transmission model we investigated the impact of the feedback between compliance, the incidence of infection, and vaccination coverage on the success of a vaccination programme in the population where waning of compliance depends on vaccine coverage. Our results suggest that the combination of fast waning compliance, slow vaccination rates, and more transmissible variants may result in a higher cumulative number of infections than in a situation without vaccination. These adverse effects can be alleviated if vaccinated individuals do not revert to pre-pandemic contact rates, and if non-vaccinated individuals remain compliant with physical distancing measures. Both require convincing, clear and appropriately targeted communication strategies by public health authorities.

Analisis Titik Kesetimbangan Dan Kestabilan Penyebaran Penyakit Malaria di Distrik Manokwari Barat Berdasarkan Model Epidemik SIR

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Fandy Fandy ◽  
Andi Fajeriani Wyrasti ◽  
Tri Widjajanti
Keyword(s):  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Endemic Diseases ◽  
Sir Epidemic

<em>Stability and equilibrium of malaria&rsquo;s epidemics in Manokwari Barat district based on SIR epidemic model will be discussed in this paper. The SIR epidemic model can be applied to make a model of endemic diseases like malaria. Based on this research, there are 2 types of the equilibrium of malaria&rsquo;s epidemics in Manokwari Barat District, endemic and non endemic point.</em>

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