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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...
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In this study, the extended SEIR dynamical model is formulated to investigate the spread of coronavirus disease (COVID-19) via a special focus on contact with asymptomatic and self-isolated infected individuals. Furthermore, a mathematical analysis of the model, including positivity, boundedness, and local and global stability of the disease-free a...
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... Their mathematical analysis did not mention any possible dynamical behavior likely to be induced by reinfection mechanism, such as the phenomenon of backward bifurcation. [18] investigated dynamics of novel COVID-19 in the presence of co-morbidity with a possibility of reinfection of recovered individuals and found that reinfection could trigger a bi-stability phenomena. However, their paper did not consider a scenario where reinfection may boost an individual natural acquired immunity. ...
... (i) What is the epidemiological implication of boosted infection-acquired immunity? In light of the revelation that reinfection among recovered individuals who have recuperated from COVID-19 can induce the phenomenon of backward bifurcation [18], we shall investigate whether incorporation of a boosted infection-acquired immunity mechanism can induce new bifurcation structures. (ii) Is there any epidemiological insights if there is heterogeneity in infection-acquired immunity among individuals who have recovered from COVID-19? ...
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.
... Before the invention of vaccines, the use of face masks, lock-down, and other non-pharmaceutical interventions and community mitigation strategies (such as: washing and sanitizing hands frequently, and isolation of suspected individuals) were thought to be the effective way to mitigate the disease spread [3,4]. These intervention measures did prove their effectiveness theoretically and mathematically against the pandemic [5,6] but were sometimes insufficient to stop the disease outbreak. So vaccination is thought to be the most effective way to confront this issue and hence vaccinologists worked tirelessly to develop vaccines for preventing At the end of 2020, the first vaccine was approved by World Health Organization (WHO) [7] and it was assumed that vaccination can lead to the end of this pandemic. ...
... Mathematical models can also be analyzed numerically to evaluate the consequences of the new SARS-CoV-2 mutants. There are lots of mathematical models to evaluate the transmission dynamics of COVID-19 [17,6,18,19,20,21,22,16,23,24] and so on. But there are only a few mathematical models to describe the behavior of the COVID-19 wild strain in the presence of its variants of concern [25,26,27,28]. ...
... 0.007, 0.009, 0.006, 0.001 Day -1 Estimated from [36] δ a 2 , δ a 3 , δ q and δ h 0.001, 0.003, 0.004, 0.006 Day -1 Estimated from [36] µ 0.00004 Day -1 [6] Condition-i of Theorem 1 says that the model with the original strain only has a unique endemic equilibrium when R 1 > 1. Using the parameter values as given in table 1 with α = 0 it can be shown that R 1 > 1 which implies there exists a unique endemic equilibrium. ...
Since its inception in December 2019, many safe and effective vaccines have been invented and approved for use against COVID-19 along with various non-pharmaceutical interventions. But the emergence of numerous SARS-CoV-2 variants has put the effectiveness of these vaccines, and other intervention measures under threat. So it is important to understand the dynamics of COVID-19 in the presence of its variants of concern (VOC) in controlling the spread of the disease. To address these situations and to find a way out of this problem, a new mathematical model consisting of a system of non-linear differential equations considering the original COVID-19 strain with its two variants of concern (Delta and Omicron) has been proposed and formulated in this paper. We then analyzed the proposed model to study the transmission dynamics of this multi-strain model and to investigate the consequences of the emergence of multiple new SARS-CoV-2 variants which are more transmissible than the previous ones. The control reproduction number, an important threshold parameter, is then calculated using the next-generation matrix method. Further, we presented the discussion about the stability of the model equilibrium. It is shown that the disease-free equilibrium (DFE) of the model is locally asymptotic stable when the control reproduction is less than unity. It is also shown that the model has a unique endemic equilibrium (EEP) which is locally asymptotic stable when the control reproduction number is greater than unity. Using the Center Manifold theory it is shown that the model also exhibits the backward bifurcation phenomenon when the control reproduction number is less than unity. Again without considering the re-infection of the recovered individuals, it is proved that the disease-free equilibrium is globally asymptotically stable when the reproduction threshold is less than unity. Finally, numerical simulations are performed to verify the analytic results and to show the impact of multiple new SARS-CoV-2 variants in the population which are more contagious than the previous variants. Global uncertainty and sensitivity analysis has been done to identify which parameters have a greater impact on disease dynamics and control disease transmission. Numerical simulation suggests that the emergence of new variants of concern increases COVID-19 infection and related deaths. It also reveals that a combination of non-pharmaceutical interventions with vaccination programs of new more effective vaccines should be continued to control the disease outbreak. This study also suggests that more doses of vaccine should provide to combat new and deadly variants like Delta and Omicron.
... A survey from the US revealed that 5-6 out of 10 adults intended to continue wearing a face mask or using other preventive measures after receiving the first dose [38]. Studies on the cessation of the use of masks in patients with diabetes after being vaccinated against COVID-19 are not available, despite the importance of discontinuing the use of face masks in any population, and even more, in patients with diabetes because of their greater predisposition to complications and risk of dying from COVID-19 [39]. Although today the use of masks is no longer mandatory in Mexico and other regions, the study of the cessation of mask use still provides essential and valuable information. ...
Studies on the cessation of face mask use after a COVID-19 vaccine in patients with diabetes are not available, despite their greater predisposition to complications. We estimated the prevalence of cessation of face mask use after receiving the COVID-19 vaccine in patients with diabetes and identified which factor was most strongly associated with non-use. This was a cross-sectional study in patients with diabetes 18–70 years with at least one dose of vaccine against COVID-19 (n = 288). Participants were asked to respond face-to-face to a questionnaire in a primary care center. Descriptive statistics, chi-square tests, and multivariate binary logistic regression were used for analyzing the association between vulnerability, benefits, barriers, self-efficacy, vaccine expectations (independent variables), and cessation of use (dependent variable), controlling for sociodemographic, smoking, medical, vaccine, and COVID-19 history. The prevalence of cessation of face masks was 25.3% (95% CI 20.2, 30.5). Not feeling vulnerable to hospitalization increased the odds of non-use (adjusted OR = 3.3, 95% CI 1.2, 8.6), while perceiving benefits did the opposite (adjusted OR = 0.4, 95% CI 0.2, 0.9). The prevalence was low, and only two factors were associated with the cessation of face mask use after COVID-19 vaccination in patients with type 2 diabetes.
... Their mathematical analysis did not mention any possible dynamical behavior likey to be induced by reinfection mechanism, such as the phenomenon of backward bifurcation. Saha et al. [18] investigated dynamics of novel COVID-19 in the presence of co-morbidity with a possibility of reinfection of recovered individuals and found that reinfection could trigger a bistability phenomena. However, their paper did not consider a scenario where reinfection may boost an individual natural acquired immunity. ...
... (i) What is the epidemiolgical implication of boosted infection-acquired immunity? In light of the revelation that reinfection among recovered indviduals who have recuperated from COVID-19 can induce the phenomenon of backward bifurcation [18], we shall investigate whether incorporation of a boosted infection-acquired immunity mechanism can induce new bifurcation structures? ...
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 co-existence 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.
SARS COV-2 (COVID-19) has a imposed remarkable socio-economic burden and its
impact is still being felt today. In the thesis paper, firstly, we have considered a de-
terministic model that emphasizes the impact of vaccination on the ongoing epidemic
and describe the dynamics of COVID-19 transmission. The suggested model takes
into account the recent findings on COVID-19, such as reinfection, waning of vacci-
nation immunity and infectiousness of those who are asymptomatic, to describe the
dynamics of the disease.
The novel coronavirus disease (COVID-19) caused by SARS-CoV-2 remains a major public health concern globally. In this article, we developed and analyzed an epidemic model of COVID-19 with the impact of vaccination governed by a five system of ordinary differential equations. The developed model is analyzed and the threshold quantity known as the effective reproduction number V R is obtained by using the next generation matrix. We investigate the equilibrium stability of the system, and the disease-free equilibrium is said to be locally asymptotically stable when the effective reproduction number is less than unity, and unstable otherwise. It is observed that the system undergoes the phenomenon of backward bifurcation. Numerical simulations of the overall system are implemented in MATLAB for demonstration of the theoretical results.
In this paper, a deterministic compartmental model is presented to assess the impact of vaccination and non-pharmaceutical interventions (social distance, awareness, face mask, and quarantine) on the transmission dynamics of COVID-19 with co-morbidity and re-infection. An expression for the basic reproduction number is then derived for this model. Theoretical analysis shows that the model exhibits backward bifurcation phenomenon when the basic reproduction number is less than unity. But for the case of no re-infection, the model has a globally asymptotically stable disease-free equilibrium (DFE) when the basic reproduction number is less than unity. Furthermore, it is shown that in the case of no re-infection, a unique endemic equilibrium point (EEP) of the model exists which is globally asymptotically stable whenever the reproduction number is greater than unity. From the global sensitivity and uncertainty analysis, we have identified mask coverage, mask efficacy, vaccine coverage, vaccine efficacy, and contact rate as the most influential parameters influencing the spread of COVID-19. Numerical simulation results show that the use of effective vaccines with proper implementation of non-pharmaceutical interventions could lead to the elimination of COVID-19 from the community. Numerical simulations also suggest that the control strategy that ensures a continuous and effective mass vaccination program is the most cost-effective control strategy. The study also shows that in the presence of any co-morbidity and with the occurrence of re-infection, the disease burden may increase.
