A generalized distributed delay model of COVID-19: An endemic model with immunity waning

An immuno-epidemiological model with waning immunity after infection or vaccination

In epidemics, waning immunity is common after infection or vaccination of individuals. Immunity levels are highly heterogeneous and dynamic. This work presents an immuno-epidemiological model that captures the fundamental dynamic features of immunity acquisition and wane after infection or vaccination and analyzes mathematically its dynamical properties. The model consists of a system of first order partial differential equations, involving nonlinear integral terms and different transfer velocities. Structurally, the equation may be interpreted as a Fokker-Planck equation for a piecewise deterministic process. However, unlike the usual models, our equation involves nonlocal effects, representing the infectivity of the whole environment. This, together with the presence of different transfer velocities, makes the proved existence of a solution novel and nontrivial. In addition, the asymptotic behavior of the model is analyzed based on the obtained qualitative properties of the solution. An optimal control problem with objective function including the total number of deaths and costs of vaccination is explored. Numerical results describe the dynamic relationship between contact rates and optimal solutions. The approach can contribute to the understanding of the dynamics of immune responses at population level and may guide public health policies.

A bifurcation analysis and model of Covid-19 transmission dynamics with post-vaccination infection impact

SARS COV-2 (Covid-19) has imposed a monumental socio-economic burden worldwide, and its impact still lingers. We propose a deterministic model to describe the transmission dynamics of Covid-19, emphasizing the effects of vaccination on the prevailing epidemic. The proposed model incorporates current information on Covid-19, such as reinfection, waning of immunity derived from the vaccine, and infectiousness of the pre-symptomatic individuals into the disease dynamics. Moreover, the model analysis reveals that it exhibits the phenomenon of backward bifurcation, thus suggesting that driving the model reproduction number below unity may not suffice to drive the epidemic toward extinction. The model is fitted to real-life data to estimate values for some of the unknown parameters. In addition, the model epidemic threshold and equilibria are determined while the criteria for the stability of each equilibrium solution are established using the Metzler approach. A sensitivity analysis of the model is performed based on the Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCCs) approaches to illustrate the impact of the various model parameters and explore the dependency of control reproduction number on its constituents parameters, which invariably gives insight on what needs to be done to contain the pandemic effectively. The foregoing notwithstanding, the contour plots of the control reproduction number concerning some of the salient parameters indicate that increasing vaccination coverage and decreasing vaccine waning rate would remarkably reduce the value of the reproduction number below unity, thus facilitating the possible elimination of the disease from the population. Finally, the model is solved numerically and simulated for different scenarios of disease outbreaks with the findings discussed.

Inappropriate therapy of euvolemic hyponatremia, the most frequent type of hyponatremia in SARS-CoV-2 infection, is associated with increased mortality in COVID-19 patients

Introduction

Admission hyponatremia, frequent in patients hospitalized for COVID-19, has been associated with increased mortality. However, although euvolemic hyponatremia secondary to the Syndrome of Inappropriate Antidiuresis (SIAD) is the single most common cause of hyponatremia in community-acquired pneumonia (CAP), a thorough and rigorous assessment of the volemia of hyponatremic COVID-19 subjects has yet to be described. We sought to identify factors contributing to mortality and hospital length-of-stay (LOS) in hospitalized COVID-19 patients admitted with hyponatremia, taking volemia into account.

Method

Retrospective study of 247 patients admitted with COVID-19 to a tertiary hospital in Madrid, Spain from March 1st through March 30th, 2020, with a glycemia-corrected serum sodium level (SNa) < 135 mmol/L. Variables were collected at admission, at 2nd-3rd day of hospitalization, and ensuing days when hyponatremia persisted. Admission volemia (based on both physical and analytical parameters), therapy, and its adequacy as a function of volemia, were determined.

Results

Age: 68 years [56-81]; 39.9% were female. Median admission SNa was 133 mmol/L [131- 134]. Hyponatremia was mild (SNa 131-134 mmol/L) in 188/247 (76%). Volemia was available in 208/247 patients; 57.2% were euvolemic and the rest (42.8%) hypovolemic. Hyponatremia was left untreated in 154/247 (62.3%) patients. Admission therapy was not concordant with volemia in 43/84 (51.2%). In fact, the majority of treated euvolemic patients received incorrect therapy with isotonic saline (37/41, 90.2%), whereas hypovolemics did not (p=0.001). The latter showed higher mortality rates than those receiving adequate or no therapy (36.7% vs. 19% respectively, p=0.023). The administration of isotonic saline to euvolemic hyponatremic subjects was independently associated with an elevation of in-hospital mortality (Odds Ratio: 3.877, 95%; Confidence Interval: 1.25-12.03).

Conclusion

Hyponatremia in COVID-19 is predominantly euvolemic. Isotonic saline infusion therapy in euvolemic hyponatremic COVID-19 patients can lead to an increased mortality rate. Thus, an exhaustive and precise volemic assessment of the hyponatremic patient with CAP, particularly when due to COVID-19, is mandatory before instauration of therapy, even when hyponatremia is mild.