Age Dependent Epidemic Modeling of COVID-19 Outbreak in Kuwait, France, and Cameroon

Hopf bifurcation in a chronological age-structured SIR epidemic model with age-dependent infectivity

In this paper, we examine the stability of an endemic equilibrium in a chronological age-structured SIR (susceptible, infectious, removed) epidemic model with age-dependent infectivity. Under the assumption that the transmission rate is a shifted exponential function, we perform a Hopf bifurcation analysis for the endemic equilibrium, which uniquely exists if the basic reproduction number is greater than 1. We show that if the force of infection in the endemic equilibrium is equal to the removal rate, then there always exists a critical value such that a Hopf bifurcation occurs when the bifurcation parameter reaches the critical value. Moreover, even in the case where the force of infection in the endemic equilibrium is not equal to the removal rate, we show that if the distance between them is sufficiently small, then a similar Hopf bifurcation can occur. By numerical simulation, we confirm a special case where the stability switch of the endemic equilibrium occurs more than once.

Mathematical Modelling of the Spatial Distribution of a COVID-19 Outbreak with Vaccination Using Diffusion Equation

The formulation of mathematical models using differential equations has become crucial in predicting the evolution of viral diseases in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China, which causes a severe and potentially fatal respiratory syndrome. Since then, it has been declared a pandemic by the World Health Organization and has spread around the globe. A reaction−diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process, in which different substances are transformed, and a diffusion process, which causes their distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic using the bias of reaction−diffusion equations. Both local and global asymptotic stability conditions for the equilibria were determined using a Lyapunov function, and the nature of the stability was determined using the Routh−Hurwitz criterion. Furthermore, we consider the conditions for the existence and uniqueness of the model solution and show the spatial distribution of the model compartments when the basic reproduction rate R0<1 and R0>1. Thereafter, we conducted a sensitivity analysis to determine the most sensitive parameters in the proposed model. We demonstrate the model’s effectiveness by performing numerical simulations and investigating the impact of vaccination, together with the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. Therefore, we offer to the public health policymakers a better understanding of COVID-19 management.

mRNA COVID-19 Vaccines-Facts and Hypotheses on Fragmentation and Encapsulation

BACKGROUND

The adventure of the mRNA vaccine began thirty years ago in the context of influenza. This consisted in encapsulating the mRNA coding for a viral protein in a lipid particle. We show how the mRNA encoding S protein has been modified for that purpose in the context of the anti-SARS-CoV-2 vaccination.

RESULTS

by using data coming from genetic and epidemiologic databases, we show the theoretical possibility of fragmentation of this mRNA into small RNA sequences capable of inhibiting important bio-syntheses such as the production of beta-globin.

DISCUSSION

we discuss two aspects related to mRNA vaccine: (i) the plausibility of mRNA fragmentation, and (ii) the role of liposomal nanoparticles (LNPs) used in the vaccine and their impact on mRNA biodistribution.

CONCLUSION

we insist on the need to develop lipid nanoparticles allowing personalized administration of vaccines and avoiding adverse effects due to mRNA fragmentation and inefficient biodistribution. Hence, we recommend (i) adapting the mRNA of vaccines to the least mutated virus proteins and (ii) personalizing its administration to the categories of chronic patients at risk most likely to suffer from adverse effects.

In-person school reopening and the spread of SARS-CoV-2 during the second wave in Spain

We investigate the effects of school reopening on the evolution of COVID-19 infections during the second wave in Spain studying both regional and age-group variation within an interrupted time-series design. Spain's 17 Autonomous Communities reopened schools at different moments in time during September 2020. We find that in-person school reopening correlates with a burst in infections in almost all those regions. Data from Spanish regions gives a further leverage: in some cases, pre-secondary and secondary education started at different dates. The analysis of those cases does not allow to conclude whether reopening one educational stage had an overall stronger impact than the other. To provide a plausible mechanism connecting school reopening with the burst in contagion, we study the Catalan case in more detail, scrutinizing the interrupted time-series patterns of infections among age-groups and the possible connections between them. The stark and sudden increase in contagion among older children (10-19) just after in-person school reopening appears to drag the evolution of other age-groups according to Granger causality. This might be taken as an indirect indication of household transmission from offspring to parents with important societal implications for the aggregate dynamics of infections.

A Model for the Lifespan Loss Due to a Viral Disease: Example of the COVID-19 Outbreak

The end of the acute phase of the COVID-19 pandemic is near in some countries as declared by World Health Organization (WHO) in January 2022 based on some studies in Europe and South Africa despite unequal distribution of vaccines to combat the disease spread globally. The heterogeneity in individual age and the reaction to biological and environmental changes that has been observed in COVID-19 dynamics in terms of different reaction to vaccination by age group, severity of infection per age group, hospitalization and Intensive Care Unit (ICU) records show different patterns, and hence, it is important to improve mathematical models for COVID-19 pandemic prediction to account for different proportions of ages in the population, which is a major factor in epidemic history. We aim in this paper to estimate, using the Usher model, the lifespan loss due to viral infection and ageing which could result in pathological events such as infectious diseases. Exploiting epidemiology and demographic data firstly from Cameroon and then from some other countries, we described the ageing in the COVID-19 outbreak in human populations and performed a graphical representation of the proportion of sensitivity of some of the model parameters which we varied. The result shows a coherence between the orders of magnitude of the calculated and observed incidence numbers during the epidemic wave, which constitutes a semi-quantitative validation of the mathematical modelling approach at the population level. To conclude, the age heterogeneity of the populations involved in the COVID-19 outbreak needs the consideration of models in age groups with specific susceptibilities to infection.