Future implications of COVID-19 through Mathematical modeling

Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses

The present study discussed a model to describe the SARS-CoV-2 viral kinetics in the presence of saturated antiviral responses. A discrete-time delay was introduced due to the time required for uninfected epithelial cells to activate a suitable antiviral response by generating immune cytokines and chemokines. We examined the system's stability at each equilibrium point. A threshold value was obtained for which the system switched from stability to instability via a Hopf bifurcation. The length of the time delay has been computed, for which the system has preserved its stability. Numerical results show that the system was stable for the faster antiviral responses of epithelial cells to the virus concentration, i.e., quick antiviral responses stabilized patients' bodies by neutralizing the virus. However, if the antiviral response of epithelial cells to the virus increased, the system became unstable, and the virus occupied the whole body, which caused patients' deaths.

Early detection of local SARS-CoV-2 outbreaks by wastewater surveillance: a feasibility study

Wastewater surveillance and quantitative analysis of SARS-CoV-2 RNA are increasingly used to monitor the spread of COVID-19 in the community. We studied the feasibility of applying the surveillance data for early detection of local outbreaks. A Monte Carlo simulation model was constructed, applying data on reported variation in RNA gene copy concentration in faeces and faecal masses shed. It showed that, even with a constant number of SARS-CoV-2 RNA shedders, the variation in concentrations found in wastewater samples will be large, and that it will be challenging to translate viral concentrations into incidence estimates, especially when the number of shedders is low. Potential signals for early detection of hypothetical outbreaks were analysed for their performance in terms of sensitivity and specificity of the signals. The results suggest that a sudden increase in incidence is not easily identified on the basis of wastewater surveillance data, especially in small sampling areas and in low-incidence situations. However, with a high number of shedders and when combining data from multiple consecutive tests, the performance of wastewater sampling is expected to improve considerably. The developed modelling approach can increase our understanding of the results from wastewater surveillance of SARS-CoV-2.

Modeling of COVID-19 spread with self-isolation at home and hospitalized classes

This work examines the impacts of self-isolation and hospitalization on the population dynamics of the Corona-Virus Disease. We developed a new nonlinear deterministic model eight classes compartment, with self-isolation and hospitalized being the most effective tools. There are (Susceptible S C ( t ) , Exposed E ( t ) , Asymptomatic infected I A ( t ) , Symptomatic infected A S ( t ) , Self-isolation T M ( t ) , Hospitalized T H ( t ) , Healed H ( t ) , and Susceptible individuals previously infected H C ( t ) ). The expression of basic reproduction number R 0 comes from the next-generation matrix method. With suitably constructed Lyapunov functions, the global asymptotic stability of the non-endemic equilibria Σ 0 for R 0 < 1 and that of endemic equilibria Σ ∗ for R 0 > 1 are established. The computed value of R 0 = 3 . 120277403 proves the endemic level of the epidemic. The outbreak will lessen if a policy is enforced like self-isolation and hospitalization. This is related to those policies that can reduce the number of direct contacts between infected and susceptible individuals or waning immunity individuals. Various simulations are presented to appreciate self-isolation at home and hospitalized strategies if applied sensibly. By performing a global sensitivity analysis, we can obtain parameter values that affect the model through a combination of Latin Hypercube Sampling and Partial Rating Correlation Coefficients methods to determine the parameters that affect the number of reproductions and the increase in the number of COVID cases. The results obtained show that the rate of self-isolation at home and the rate of hospitalism have a negative relationship. On the other hand, infections will decrease when the two parameters increase. From the sensitivity of the results, we formulate a control model using optimal control theory by considering two control variables. The result shows that the control strategies minimize the spread of the COVID infection in the population.

Modeling time evolving COVID-19 uncertainties with density dependent asymptomatic infections and social reinforcement

The COVID-19 pandemic has posed significant challenges in modeling its complex epidemic transmissions, infection and contagion, which are very different from known epidemics. The challenges in quantifying COVID-19 complexities include effectively modeling its process and data uncertainties. The uncertainties are embedded in implicit and high-proportional undocumented infections, asymptomatic contagion, social reinforcement of infections, and various quality issues in the reported data. These uncertainties become even more apparent in the first 2 months of the COVID-19 pandemic, when the relevant knowledge, case reporting and testing were all limited. Here we introduce a novel hybrid approach SUDR by expanding the foundational compartmental epidemic Susceptible-Infected-Recovered (SIR) model with two compartments to a Susceptible-Undocumented infected-Documented infected-Recovered (SUDR) model. First, SUDR (1) characterizes and distinguishes Undocumented (U) and Documented (D) infections commonly seen during COVID-19 incubation periods and asymptomatic infections. Second, SUDR characterizes the probabilistic density of infections by capturing exogenous processes like clustering contagion interactions, superspreading, and social reinforcement. Lastly, SUDR approximates the density likelihood of COVID-19 prevalence over time by incorporating Bayesian inference into SUDR. Different from existing COVID-19 models, SUDR characterizes the undocumented infections during unknown transmission processes. To capture the uncertainties of temporal transmission and social reinforcement during COVID-19 contagion, the transmission rate is modeled by a time-varying density function of undocumented infectious cases. By sampling from the mean-field posterior distribution with reasonable priors, SUDR handles the randomness, noise and sparsity of COVID-19 observations widely seen in the public COVID-19 case data. The results demonstrate a deeper quantitative understanding of the above uncertainties, in comparison with classic SIR, time-dependent SIR, and probabilistic SIR models.