ArticlePublisher preview available

Emergence of a reversed backward bifurcation, reversed hysteresis effect, and backward bifurcation phenomenon in a COVID‐19 mathematical model

Authors:
Isaac Mwangi at Laikipia University
Isaac Mwangi
Read publisher preview
Download citation
To read the full-text of this research, you can request a copy directly from the author.

Abstract and Figures

A coronavirus disease 2019 (COVID‐19) epidemiological model incorporating a boosted infection‐acquired immunity and heterogeneity in infection‐acquired immunity among recovered individuals is designed. The model is used to investigate whether incorporating these two processes can induce new epidemiological insights. Analytical findings reveal coexistence of multiple endemic equilibria on either regions divided by the fundamental threshold (control reproduction number). Numerical findings conducted to validate analytical results show that heterogeneity in infection‐acquired immunity among recovered individuals can induce various bifurcation structures such as reversed backward bifurcation , forward bifurcation , backward bifurcation , and reversed hysteresis effect. Moreover, numerical results show that reversed backward bifurcation is annihilated or switches to the usual forward bifurcation if infection‐acquired immunity among recovered individuals with strong immunity is assumed to be everlasting. However, this is only possible if primary infection is more likely than reinfection. In case reinfection is more likely to occur than primary infection, reversed backward bifurcation structure switches to a backward bifurcation phenomenon. Further, longer duration of infection‐acquired immunity does lead to COVID‐19 decline over time but does not lead to flattening of the COVID‐19 peak.
A flow diagram representing epidemiological status and the respective parameters that indicate rates of transition from one health status to another. The magenta‐filled compartment represents recovered individuals whose infection‐acquired immunity is partial and these individuals can be reinfected upon re‐exposure with COVID‐19. The green‐filled compartment represents recovered individuals whose infection‐acquired immunity is strong enough to resist reinfection. [Colour figure can be viewed at wileyonlinelibrary.com]
A flow diagram representing epidemiological status and the respective parameters that indicate rates of transition from one health status to another. The magenta‐filled compartment represents recovered individuals whose infection‐acquired immunity is partial and these individuals can be reinfected upon re‐exposure with COVID‐19. The green‐filled compartment represents recovered individuals whose infection‐acquired immunity is strong enough to resist reinfection. [Colour figure can be viewed at wileyonlinelibrary.com]
… 
Illustration of the type of bifurcation structures exhibited by the model system (2). Parameters used to generate figures are the baseline parameters depicted in Table 4 except those shown in the figures. In all the figures, β∗=0.212$$ {\beta}&#x0005E;{\ast }&#x0003D;0.212 $$ corresponds to Rc=1.$$ {R}_c&#x0003D;1. $$ (A) A reversed backward bifurcation phenomenon for δ=0.5$$ \delta &#x0003D;0.5 $$, which correspond to δ(1−ϕ)=0.4991<δc=1.0004.$$ \delta \left(1-\phi \right)&#x0003D;0.4991&lt;{\delta}_c&#x0003D;1.0004. $$ (B) The structural change of reversed backward bifurcation to the usual forward bifurcation whenever reinfection does not boost an individual infection‐acquired immunity (i.e., ϕ=1$$ \phi &#x0003D;1 $$) and when reinfection does not occur (i.e., δ=0$$ \delta &#x0003D;0 $$). (C) The impact of increasing the proportion ϕ$$ \phi $$ of recovered individuals with partial infection‐acquired immunity at intermediate values (0<ϕ<1).$$ \left(0&lt;\phi &lt;1\right). $$ (D) Effect of increasing parameter f$$ f $$ (0<f<1).$$ \left(0&lt;f&lt;1\right). $$ (E) The impact of varying the duration of infection‐acquired immunity. (F) A reversed backward bifurcation phenomenon can occur even when ϕ=0$$ \phi &#x0003D;0 $$. [Colour figure can be viewed at wileyonlinelibrary.com]
Illustration of the type of bifurcation structures exhibited by the model system (2). Parameters used to generate figures are the baseline parameters depicted in Table 4 except those shown in the figures. In all the figures, β∗=0.212$$ {\beta}&#x0005E;{\ast }&#x0003D;0.212 $$ corresponds to Rc=1.$$ {R}_c&#x0003D;1. $$ (A) A reversed backward bifurcation phenomenon for δ=0.5$$ \delta &#x0003D;0.5 $$, which correspond to δ(1−ϕ)=0.4991<δc=1.0004.$$ \delta \left(1-\phi \right)&#x0003D;0.4991&lt;{\delta}_c&#x0003D;1.0004. $$ (B) The structural change of reversed backward bifurcation to the usual forward bifurcation whenever reinfection does not boost an individual infection‐acquired immunity (i.e., ϕ=1$$ \phi &#x0003D;1 $$) and when reinfection does not occur (i.e., δ=0$$ \delta &#x0003D;0 $$). (C) The impact of increasing the proportion ϕ$$ \phi $$ of recovered individuals with partial infection‐acquired immunity at intermediate values (0<ϕ<1).$$ \left(0&lt;\phi &lt;1\right). $$ (D) Effect of increasing parameter f$$ f $$ (0<f<1).$$ \left(0&lt;f&lt;1\right). $$ (E) The impact of varying the duration of infection‐acquired immunity. (F) A reversed backward bifurcation phenomenon can occur even when ϕ=0$$ \phi &#x0003D;0 $$. [Colour figure can be viewed at wileyonlinelibrary.com]
… 
Illustration of the typical forward bifurcation and the backward bifurcation structures when the recovered individuals in R2$$ {R}_2 $$ class are assumed to acquire an everlasting infection‐acquired immunity (i.e., α=0$$ \alpha &#x0003D;0 $$). The parameters used are the baseline parameters shown in Table 4. (A) Forward bifurcation when δ=0.5$$ \delta &#x0003D;0.5 $$, which correspond to δ(1−ϕ)=0.4991<δc=1.0004.$$ \delta \left(1-\phi \right)&#x0003D;0.4991&lt;{\delta}_c&#x0003D;1.0004. $$ (B) Backward bifurcation for δ=2$$ \delta &#x0003D;2 $$, which corresponds to δ(1−ϕ)=1.9980>δc=1.0004$$ \delta \left(1-\phi \right)&#x0003D;1.9980&gt;{\delta}_c&#x0003D;1.0004 $$. [Colour figure can be viewed at wileyonlinelibrary.com]
Illustration of the typical forward bifurcation and the backward bifurcation structures when the recovered individuals in R2$$ {R}_2 $$ class are assumed to acquire an everlasting infection‐acquired immunity (i.e., α=0$$ \alpha &#x0003D;0 $$). The parameters used are the baseline parameters shown in Table 4. (A) Forward bifurcation when δ=0.5$$ \delta &#x0003D;0.5 $$, which correspond to δ(1−ϕ)=0.4991<δc=1.0004.$$ \delta \left(1-\phi \right)&#x0003D;0.4991&lt;{\delta}_c&#x0003D;1.0004. $$ (B) Backward bifurcation for δ=2$$ \delta &#x0003D;2 $$, which corresponds to δ(1−ϕ)=1.9980>δc=1.0004$$ \delta \left(1-\phi \right)&#x0003D;1.9980&gt;{\delta}_c&#x0003D;1.0004 $$. [Colour figure can be viewed at wileyonlinelibrary.com]
… 
Illustration of the scenario where there is no heterogeneity in recovery among infected individuals. (A) Bifurcation structure for the case f=0$$ f&#x0003D;0 $$; that is, infected individuals who do not succumb to COVID‐19 all recover with partial/weak infection‐acquired immunity and therefore progress to R1$$ {R}_1 $$ that consists of individuals who are prone to reinfection. Parameters used remain as the baseline parameters shown in Table 4 except f=0$$ f&#x0003D;0 $$ is shown in the figure. For a better view, semi‐logarithmic scale is used. (B) Bifurcation structure (pronounced reversed backward bifurcation) for the case f=1$$ f&#x0003D;1 $$; that is, infected individuals who do not succumb due to COVID‐19 all recover with strong temporary infection‐acquired immunity. Parameters used remain as shown in Table 4 except f=1$$ f&#x0003D;1 $$ is shown in the figure. For a better view, a logarithmic scale is used on both axis. [Colour figure can be viewed at wileyonlinelibrary.com]
Illustration of the scenario where there is no heterogeneity in recovery among infected individuals. (A) Bifurcation structure for the case f=0$$ f&#x0003D;0 $$; that is, infected individuals who do not succumb to COVID‐19 all recover with partial/weak infection‐acquired immunity and therefore progress to R1$$ {R}_1 $$ that consists of individuals who are prone to reinfection. Parameters used remain as the baseline parameters shown in Table 4 except f=0$$ f&#x0003D;0 $$ is shown in the figure. For a better view, semi‐logarithmic scale is used. (B) Bifurcation structure (pronounced reversed backward bifurcation) for the case f=1$$ f&#x0003D;1 $$; that is, infected individuals who do not succumb due to COVID‐19 all recover with strong temporary infection‐acquired immunity. Parameters used remain as shown in Table 4 except f=1$$ f&#x0003D;1 $$ is shown in the figure. For a better view, a logarithmic scale is used on both axis. [Colour figure can be viewed at wileyonlinelibrary.com]
… 
The impact of readjusting the modification parameter that accounts for reinfection among recovered individuals with partial immunity such that δ≥1$$ \delta \ge 1 $$. Parameter values used to generate the figures remain as baseline parameters shown in Table 4 except that β$$ \beta $$ is varied within the interval β∈[0.001,4].$$ \beta \in \left[\mathrm{0.001,4}\right]. $$ Blue solid curves represent stable endemic curves while solid and dotted red curves represent unstable endemic curves. For a better view, semi‐logarithmic scales are used on all figures. (A) The reversed backward bifurcation when δ=1.$$ \delta &#x0003D;1. $$ (B) A reversed hysteresis effect that occurs when δ=2$$ \delta &#x0003D;2 $$ and δ(1−ϕ)=1.9980>δc=1.0004.$$ \delta \left(1-\phi \right)&#x0003D;1.9980&gt;{\delta}_c&#x0003D;1.0004. $$ (C) A reversed hysteresis effect when δ=3$$ \delta &#x0003D;3 $$ and δ(1−ϕ)=2.997>δc=1.0004.$$ \delta \left(1-\phi \right)&#x0003D;2.997&gt;{\delta}_c&#x0003D;1.0004. $$ (D) A hysteresis effect bifurcation structure for δ=4$$ \delta &#x0003D;4 $$ and δ(1−ϕ)=3.9960>δc=1.0004$$ \delta \left(1-\phi \right)&#x0003D;3.9960&gt;{\delta}_c&#x0003D;1.0004 $$. [Colour figure can be viewed at wileyonlinelibrary.com]
+5
The impact of readjusting the modification parameter that accounts for reinfection among recovered individuals with partial immunity such that δ≥1$$ \delta \ge 1 $$. Parameter values used to generate the figures remain as baseline parameters shown in Table 4 except that β$$ \beta $$ is varied within the interval β∈[0.001,4].$$ \beta \in \left[\mathrm{0.001,4}\right]. $$ Blue solid curves represent stable endemic curves while solid and dotted red curves represent unstable endemic curves. For a better view, semi‐logarithmic scales are used on all figures. (A) The reversed backward bifurcation when δ=1.$$ \delta &#x0003D;1. $$ (B) A reversed hysteresis effect that occurs when δ=2$$ \delta &#x0003D;2 $$ and δ(1−ϕ)=1.9980>δc=1.0004.$$ \delta \left(1-\phi \right)&#x0003D;1.9980&gt;{\delta}_c&#x0003D;1.0004. $$ (C) A reversed hysteresis effect when δ=3$$ \delta &#x0003D;3 $$ and δ(1−ϕ)=2.997>δc=1.0004.$$ \delta \left(1-\phi \right)&#x0003D;2.997&gt;{\delta}_c&#x0003D;1.0004. $$ (D) A hysteresis effect bifurcation structure for δ=4$$ \delta &#x0003D;4 $$ and δ(1−ϕ)=3.9960>δc=1.0004$$ \delta \left(1-\phi \right)&#x0003D;3.9960&gt;{\delta}_c&#x0003D;1.0004 $$. [Colour figure can be viewed at wileyonlinelibrary.com]
… 
Figures - available from: Mathematical Methods in the Applied Sciences
This content is subject to copyright. Terms and conditions apply.
A preview of this full-text is provided by Wiley.
Learn more
Content available from Mathematical Methods in the Applied Sciences
This content is subject to copyright. Terms and conditions apply.
Received: 19 November 2022 Accepted: 7 October 2023
DOI: 10.1002/mma.9745
RESEARCH ARTICLE
Emergence of a reversed backward bifurcation, reversed
hysteresis effect, and backward bifurcation phenomenon in
a COVID-19 mathematical model
Isaac Mwangi Wangari
Department of Mathematics and
Computing Science, School of Pure and
Applied Sciences, Bomet University
College, Bomet, Kenya
Correspondence
Isaac Mwangi Wangari, Department of
Mathematics and Computing Science,
School of Pure and Applied Sciences,
Bomet University College, PO Box
701-20400, Bomet, Kenya.
Email: mwangiisaac@aims.ac.za
Communicated by: M. Efendiev
Funding information
There are no funders to report for this
submission.
A coronavirus disease 2019 (COVID-19) epidemiological model incorporating
a boosted infection-acquired immunity and heterogeneity in infection-acquired
immunity among recovered individuals is designed. The model is used to investi-
gate whether incorporating these two processes can induce new epidemiological
insights. Analytical findings reveal coexistence of multiple endemic equilibria
on either regions divided by the fundamental threshold (control reproduction
number). Numerical findings conducted to validate analytical results show that
heterogeneity in infection-acquired immunity among recovered individuals can
induce various bifurcation structures such as reversed backward bifurcation,
forward bifurcation,backward bifurcation,andreversed hysteresis effect. More-
over, numerical results show that reversed backward bifurcation is annihilated or
switches to the usual forward bifurcation if infection-acquired immunity among
recovered individuals with strong immunity is assumed to be everlasting. How-
ever, this is only possible if primary infection is more likely than reinfection. In
case reinfection is more likely to occur than primary infection, reversed backward
bifurcation structure switches to a backward bifurcation phenomenon. Further,
longer duration of infection-acquired immunity does lead to COVID-19 decline
over time but does not lead to flattening of the COVID-19 peak.
KEYWORDS
heterogeneity, immune boosting, re-exposure, reversed backward bifurcation, reversed hysteresis
effect
MSC CLASSIFICATION
00A69, 37N25
1INTRODUCTION
The news about the spread of a novel coronavirus identified as severe acute respiratory syndrome coronavirus 2
(SARS-CoV-2) became ubiquitous across the globe in December 2019, and shortly thereafter, the disease associated with
the virus was named by World Health Organization (WHO) as coronavirus disease 2019 (or COVID-19) [1]. WHO declared
COVID-19 a global pandemic on March 11, 2020 [2]. Official data from the WHO showed that, as of July 14, 2020, there
were approximately 12,768,307 confirmed cases with 566,654 having succumbed to COVID-19-related complications [3].
Over a period of 6 months, about 105 million positive cases were confirmed, with 2.29 million deaths as of February
5, 2021. The pandemic continues to unfold, although at a slower pace in comparison to early onset of COVID-19.
Currently, there is a global concern regarding deciphering the extent of protection against emerging SARS-CoV-2
Math. Meth. Appl. Sci. 2024;47:2250–2272.wileyonlinelibrary.com/journal/mma© 2023 John Wiley & Sons, Ltd.
2250
... To effectively control these diseases, we need to thoroughly understand the immune response against the pathogens involved. In ongoing research, a phenomenon known as backward bifurcation has attracted more and more attention, particularly in the context of decline of immunity associated with EIDs [3]. In mathematical epidemiology, a backward bifurcation occurs when the basic reproduction number is less than unity, in which case a small positive unstable endemic equilibrium appears while the disease-free equilibrium and a larger positive endemic equilibrium are locally asymptotically stable [4][5][6][7]. ...
... where the expression of a is given in (3). Hence, the bifurcation at (φ,β) = (P 0 ,β * ) is transcritical, and the sign of a determines the criticality of the bifurcation, cf., e.g., [5,12]. ...
Backward bifurcation arising from decline of immunity against emerging infectious diseases
Preprint
  • Jun 2024
Decline of immunity is a phenomenon characterized by immunocompromised host and plays a crucial role in the epidemiology of emerging infectious diseases (EIDs) such as COVID-19. In this paper, we propose an age-structured model with vaccination and reinfection of immune individuals. We prove that the disease-free equilibrium of the model undergoes backward and forward transcritical bifurcations at the critical value of the basic reproduction number for different values of parameters. We illustrate the results by numerical computations, and also find that the endemic equilibrium exhibits a saddle-node bifurcation on the extended branch of the forward transcritical bifurcation. These results allow us to understand the interplay between the decline of immunity and EIDs, and are able to provide strategies for mitigating the impact of EIDs on global health.
View
Backward bifurcation arising from decline of immunity against emerging infectious diseases
Article
  • Jul 2024
  • APPL MATH LETT
Decline of immunity is a phenomenon characterized by immunocompromised host and plays a crucial role in the epidemiology of emerging infectious diseases (EIDs) such as COVID-19. In this paper, we propose an age-structured model with vaccination and reinfection of immune individuals. We prove that the disease-free equilibrium of the model undergoes backward and forward transcritical bifurcations at the critical value of the basic reproduction number for different values of parameters. We illustrate the results by numerical computations, and also find that the endemic equilibrium exhibits a saddle–node bifurcation on the extended branch of the forward transcritical bifurcation. These results allow us to understand the interplay between the decline of immunity and EIDs, and are able to provide strategies for mitigating the impact of EIDs on global health.
View
Dynamic of a two-strain COVID-19 model with vaccination
Article
Full-text available
  • Jul 2022
COVID-19 is a respiratory illness caused by an ribonucleic acid (RNA) virus prone to mutations. In December 2020, variants with different characteristics that could affect transmissibility emerged around the world. To address this new dynamic of the disease, we formulate and analyze a mathematical model of a two-strain COVID-19 transmission dynamics with strain 1 vaccination. The model is theoretically analyzed and sufficient conditions for the stability of its equilibria are derived. In addition to the disease-free and endemic equilibria, the model also has single-strain 1 and strain 2 endemic equilibria. Using the center manifold theory, it is shown that the model does not exhibit the phenomenon of backward bifurcation, and global stability of the model equilibria are proved using various approaches. Simulations to support the model theoretical results are provided. We calculate the basic reproductive number 1 and 2 for both strains independently. Results indicate that-both strains will persist when 1 > 1 and 2 > 1-Stain 2 could establish itself as the dominant strain if 1 < 1 and 2 > 1, or when 2 > 1 > 1. However, because of de novo herd immunity due to strain 1 vaccine efficacy and provided the initial stain 2 transmission threshold parameter 2 is controlled to remain below unity, strain 2 will not establish itself/persist in the community.
View
Dynamics of novel COVID-19 in the presence of Co-morbidity
Article
Full-text available
  • May 2022
A novel coronavirus (COVID-19) has emerged as a global serious public health issue from December 2019. People having a weak immune system are more susceptible to coronavirus infection. It is a double challenge for people of any age with certain underlying medical conditions including cardiovascular disease, diabetes, high blood pressure and cancer etc. Co-morbidity increases the probability of COVID-19 complication. In this paper a deterministic compartmental model is formulated to understand the transmission dynamics of COVID-19. Rigorous mathematical analysis of the model shows that it exhibits backward bifurcation phenomenon when the basic reproduction number is less than unity. For the case of no re-infection it is shown that having the reproduction number less than one is necessary and sufficient for the effective control of COVID-19, that is, the disease free equilibrium is globally asymptotically stable when the reproduction threshold is less than unity. Furthermore, in the absence of reinfection, a unique endemic equilibrium of the model exists which is globally asymptotically stable whenever the reproduction number is greater than unity. Numerical simulations of the model, using data relevant to COVID-19 transmission dynamics, show that the use of efficacious face masks publicly could lead to the elimination of COVID-19 up to a satisfactory level. The study also shows that in the presence of co-morbidity, the disease increases significantly.
View
Multiple COVID-19 Waves and Vaccination Effectiveness in the United States
Article
Full-text available
(1) Background: The coronavirus 2019 (COVID-19) pandemic has caused multiple waves of cases and deaths in the United States (US). The wild strain, the Alpha variant (B.1.1.7) and the Delta variant (B.1.617.2) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) were the principal culprits behind these waves. To mitigate the pandemic, the vaccination campaign was started in January 2021. While the vaccine efficacy is less than 1, breakthrough infections were reported. This work aims to examine the effects of the vaccination across 50 US states and the District of Columbia. (2) Methods: Based on the classic Susceptible—Exposed—Infectious–Recovered (SEIR) model, we add a delay class between infectious and death, a death class and a vaccinated class. We compare two special cases of our new model to simulate the effects of the vaccination. The first case expounds the vaccinated individuals with full protection or not, compared to the second case where all vaccinated individuals have the same level of protection. (3) Results: Through fitting the two approaches to reported COVID-19 deaths in all 50 US states and the District of Columbia, we found that these two approaches are equivalent. We calculate that the death toll could be 1.67–3.33 fold in most states if the vaccine was not available. The median and mean infection fatality ratio are estimated to be approximately 0.6 and 0.7%. (4) Conclusions: The two approaches we compared were equivalent in evaluating the effectiveness of the vaccination campaign in the US. In addition, the effect of the vaccination campaign was significant, with a large number of deaths averted.
View
COVID-19 reinfections among naturally infected and vaccinated individuals
Article
Full-text available
  • Jan 2022
The protection against emerging SARS-CoV-2 variants by pre-existing antibodies elicited due to the current vaccination or natural infection is a global concern. We aimed to investigate the rate of SARS-CoV-2 infection and its clinical features among infection-naïve, infected, vaccinated, and post-infection-vaccinated individuals. A cohort was designed among icddr,b staff registered for COVID-19 testing by real-time reverse transcriptase-polymerase chain reaction (rRT-PCR). Reinfection cases were confirmed by whole-genome sequencing. From 19 March 2020 to 31 March 2021, 1644 (mean age, 38.4 years and 57% male) participants were enrolled; where 1080 (65.7%) were tested negative and added to the negative cohort. The positive cohort included 750 positive patients (564 from baseline and 186 from negative cohort follow-up), of whom 27.6% were hospitalized and 2.5% died. Among hospitalized patients, 45.9% had severe to critical disease and 42.5% required oxygen support. Hypertension and diabetes mellitus were found significantly higher among the hospitalised patients compared to outpatients ; risk ratio 1.3 and 1.6 respectively. The risk of infection among positive cohort was 80.2% lower than negative cohort (95% CI 72.6-85.7%; p < 0.001). Genome sequences showed that genetically distinct SARS-CoV-2 strains were responsible for reinfections. Naturally infected populations were less likely to be reinfected by SARS-CoV-2 than the infection-naïve and vaccinated individuals. Although, reinfected individuals did not suffer severe disease, a remarkable proportion of naturally infected or vaccinated individuals were (re)-infected by the emerging variants.
View
The impact of infection-derived immunity on disease dynamics
Article
Full-text available
  • Dec 2021
  • J MATH BIOL
When modeling infectious diseases, it is common to assume that infection-derived immunity is either (1) non-existent or (2) perfect and lifelong. However there are many diseases in which infection-derived immunity is known to be present but imperfect. There are various ways in which infection-derived immunity can fail, which can ultimately impact the probability that an individual be reinfected by the same pathogen, as well as the long-run population-level prevalence of the pathogen. Here we discuss seven different models of imperfect infection-derived immunity, including waning, leaky and all-or-nothing immunity. For each model we derive the probability that an infected individual becomes reinfected during their lifetime, given that the system is at endemic equilibrium. This can be thought of as the impact that each of these infection-derived immunity failures have on reinfection. This measure is useful because it provides us with a way to compare different modes of failure of infection-derived immunity.
View
Mathematical Modelling of COVID-19 Transmission in Kenya: A Model with Reinfection Transmission Mechanism
Article
Full-text available
  • Oct 2021
In this study we propose a Coronavirus Disease 2019 (COVID-19) mathematical model that stratifies infectious subpopulations into: infectious asymptomatic individuals, symptomatic infectious individuals who manifest mild symptoms and symptomatic individuals with severe symptoms. In light of the recent revelation that reinfection by COVID-19 is possible, the proposed model attempt to investigate how reinfection with COVID-19 will alter the future dynamics of the recent unfolding pandemic. Fitting the mathematical model on the Kenya COVID-19 dataset, model parameter values were obtained and used to conduct numerical simulations. Numerical results suggest that reinfection of recovered individuals who have lost their protective immunity will create a large pool of asymptomatic infectious individuals which will ultimately increase symptomatic individuals with mild symptoms and symptomatic individuals with severe symptoms (critically ill) needing urgent medical attention. The model suggests that reinfection with COVID-19 will lead to an increase in cumulative reported deaths. Comparison of the impact of non pharmaceutical interventions on curbing COVID19 proliferation suggests that wearing face masks profoundly reduce COVID-19 prevalence than maintaining social/physical distance. Further, numerical findings reveal that increasing detection rate of asymptomatic cases via contact tracing, testing and isolating them can drastically reduce COVID-19 surge, in particular individuals who are critically ill and require admission into intensive care.
View
Assessment of protection against reinfection with SARS-CoV-2 among 4 million PCR-tested individuals in Denmark in 2020: a population-level observational study
Article
Full-text available
  • Mar 2021
Background The degree to which infection with SARS-CoV-2 confers protection towards subsequent reinfection is not well described. In 2020, as part of Denmark's extensive, free-of-charge PCR-testing strategy, approximately 4 million individuals (69% of the population) underwent 10·6 million tests. Using these national PCR-test data from 2020, we estimated protection towards repeat infection with SARS-CoV-2. Methods In this population-level observational study, we collected individual-level data on patients who had been tested in Denmark in 2020 from the Danish Microbiology Database and analysed infection rates during the second surge of the COVID-19 epidemic, from Sept 1 to Dec 31, 2020, by comparison of infection rates between individuals with positive and negative PCR tests during the first surge (March to May, 2020). For the main analysis, we excluded people who tested positive for the first time between the two surges and those who died before the second surge. We did an alternative cohort analysis, in which we compared infection rates throughout the year between those with and without a previous confirmed infection at least 3 months earlier, irrespective of date. We also investigated whether differences were found by age group, sex, and time since infection in the alternative cohort analysis. We calculated rate ratios (RRs) adjusted for potential confounders and estimated protection against repeat infection as 1 – RR. Findings During the first surge (ie, before June, 2020), 533 381 people were tested, of whom 11 727 (2·20%) were PCR positive, and 525 339 were eligible for follow-up in the second surge, of whom 11 068 (2·11%) had tested positive during the first surge. Among eligible PCR-positive individuals from the first surge of the epidemic, 72 (0·65% [95% CI 0·51–0·82]) tested positive again during the second surge compared with 16 819 (3·27% [3·22–3·32]) of 514 271 who tested negative during the first surge (adjusted RR 0·195 [95% CI 0·155–0·246]). Protection against repeat infection was 80·5% (95% CI 75·4–84·5). The alternative cohort analysis gave similar estimates (adjusted RR 0·212 [0·179–0·251], estimated protection 78·8% [74·9–82·1]). In the alternative cohort analysis, among those aged 65 years and older, observed protection against repeat infection was 47·1% (95% CI 24·7–62·8). We found no difference in estimated protection against repeat infection by sex (male 78·4% [72·1–83·2] vs female 79·1% [73·9–83·3]) or evidence of waning protection over time (3–6 months of follow-up 79·3% [74·4–83·3] vs ≥7 months of follow-up 77·7% [70·9–82·9]). Interpretation Our findings could inform decisions on which groups should be vaccinated and advocate for vaccination of previously infected individuals because natural protection, especially among older people, cannot be relied on. Funding None.
View
Immunological memory to SARS-CoV-2 assessed for up to 8 months after infection
Article
Full-text available
  • Jan 2021
Variable memory Immune memory against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) helps to determine protection against reinfection, disease risk, and vaccine efficacy. Using 188 human cases across the range of severity of COVID-19, Dan et al. analyzed cross-sectional data describing the dynamics of SARS-CoV-2 memory B cells, CD8 ⁺ T cells, and CD4 ⁺ T cells for more than 6 months after infection. The authors found a high degree of heterogeneity in the magnitude of adaptive immune responses that persisted into the immune memory phase to the virus. However, immune memory in three immunological compartments remained measurable in greater than 90% of subjects for more than 5 months after infection. Despite the heterogeneity of immune responses, these results show that durable immunity against secondary COVID-19 disease is a possibility for most individuals. Science , this issue p. eabf4063
View
Scenario Analysis of COVID-19 Transmission Dynamics in Malaysia with the Possibility of Reinfection and Limited Medical Resources Scenarios
Article
  • Apr 2021
  • COMPUT BIOL MED
COVID-19 is a major health threat across the globe, which causes severe acute respiratory syndrome (SARS), and it is highly contagious with significant mortality. In this study, we conduct a scenario analysis for COVID-19 in Malaysia using a simple universality class of the SIR system and extensions thereof (i.e., the inclusion of temporary immunity through the reinfection problems and limited medical resources scenarios leads to the SIRS-type model). This system has been employed in order to provide further insights on the long-term outcomes of COVID-19 pandemic. As a case study, the COVID-19 transmission dynamics are investigated using daily confirmed cases in Malaysia, where some of the epidemiological parameters of this system are estimated based on the fitting of the model to real COVID-19 data released by the Ministry of Health Malaysia (MOH). We observe that this model is able to mimic the trend of infection trajectories of COVID-19 pandemic in Malaysia and it is possible for transmission dynamics to be influenced by the reinfection force and limited medical resources problems. A rebound effect in transmission could occur after several years and this situation depends on the intensity of reinfection force. Our analysis also depicts the existence of a critical value in reinfection threshold beyond which the infection dynamics persist and the COVID-19 outbreaks are rather hard to eradicate. Therefore, understanding the interplay between distinct epidemiological factors using mathematical modelling approaches could help to support authorities in making informed decisions so as to control the spread of this pandemic effectively.
View
SIRSi compartmental model for COVID-19 pandemic with immunity loss
Article
  • Oct 2020
  • CHAOS SOLITON FRACT
The coronavirus disease 2019 (Covid-19) outbreak led the world to an unprecedented health and economic crisis. In an attempt to respond to this emergency, researchers worldwide are intensively studying the dynamics of the Covid-19 pandemic. In this study, a Susceptible - Infected - Removed - Sick (SIRSi) compartmental model is proposed, which is a modification of the classical Susceptible - Infected - Removed (SIR) model. The proposed model considers the possibility of unreported or asymptomatic cases, and differences in the immunity within a population, i.e., the possibility that the acquired immunity may be temporary, which occurs when adopting one of the parameters ( ) other than zero. Local asymptotic stability and endemic equilibrium conditions are proved for the proposed model. The model is adjusted to the data from three major cities of the state of São Paulo in Brazil, namely, São Paulo, Santos, and Campinas, providing estimations of duration and peaks related to the disease propagation. This study reveals that temporary immunity favors a second wave of infection and it depends on the time interval for a recovered person to be susceptible again. It also indicates the possibility that a greater number of patients would get infected with decreased time for reinfection.
View