Global Analysis and Optimal Control Model of COVID-19

Influence of waning immunity on vaccination decision-making: A multi-strain epidemic model with an evolutionary approach analyzing cost and efficacy

In this research, we introduce a comprehensive epidemiological model that accounts for multiple strains of an infectious disease and two distinct vaccination options. Vaccination stands out as the most effective means to prevent and manage infectious diseases. However, when there are various vaccines available, each with its costs and effectiveness, the decision-making process for individuals becomes paramount. Furthermore, the factor of waning immunity following vaccination also plays a significant role in influencing these choices. To understand how individuals make decisions in the context of multiple strains and waning immunity, we employ a behavioral model, allowing an epidemiological model to be coupled with the dynamics of a decision-making process. Individuals base their choice of vaccination on factors such as the total number of infected individuals and the cost-effectiveness of the vaccine. Our findings indicate that as waning immunity increases, people tend to prioritize vaccines with higher costs and greater efficacy. Moreover, when more contagious strains are present, the equilibrium in vaccine adoption is reached more rapidly. Finally, we delve into the social dilemma inherent in our model by quantifying the social efficiency deficit (SED) under various parameter combinations.

Potential for eliminating COVID-19 in Thailand through third-dose vaccination: A modeling approach

The COVID-19 pandemic continues to pose significant challenges to global public health, necessitating the development of effective vaccination strategies to mitigate disease transmission. In Thailand, the COVID-19 epidemic has undergone multiple waves, prompting the implementation of various control measures, including vaccination campaigns. Understanding the dynamics of disease transmission and the impact of vaccination strategies is crucial for guiding public health interventions and optimizing epidemic control efforts. In this study, we developed a comprehensive mathematical model, termed $ S{S}_{v}I{H}_{1}C{H}_{2}RD $, to elucidate the dynamics of the COVID-19 epidemic in Thailand. The model incorporates key epidemiological parameters, vaccination rates, and disease progression stages to assess the effectiveness of different vaccination strategies in curbing disease transmission. Parameter estimation and model fitting were conducted using real-world data from COVID-19 patients in Thailand, enabling the simulation of epidemic scenarios and the exploration of optimal vaccination rates. Our results showed that optimizing vaccination strategies, particularly by administering approximately 119,625 doses per day, can significantly reduce the basic reproduction number ($ {R}_{0} $) below 1, thereby accelerating epidemic control. Simulation results demonstrated that the optimal vaccination rate led to a substantial decrease in the number of infections, with the epidemic projected to be completely eradicated from the population by June 19, 2022. These findings underscore the importance of targeted vaccination efforts and proactive public health interventions in mitigating the spread of COVID-19 and minimizing the burden on healthcare systems. Our study provides valuable insights into the optimization of vaccination strategies for epidemic control, offering guidance for policymakers and healthcare authorities in Thailand and beyond. By leveraging mathematical modeling techniques and real-world data, stakeholders can develop evidence-based strategies to combat the COVID-19 pandemic and safeguard public health.

Numerical Scheme for Compartmental Models: New Matlab Software Codes for Numerical Simulation

Background: This paper presents a newly developed Matlab code for the numerical simulation of compartmental/deterministic models. It addresses modeling and simulation issues concerning compartmental models. The code is easy to understand and edit for the simulation of compartmental models. An alternative codes for statistical software package R has been proposed for the same model. R software is freely available for use. Methods: We proposed a basic SEIR model for illustration purposes. Matlab and R software codes are developed for the SEIR model which users can follow and easily understand the computations. Results: The two codes work on all Matlab and R versions. For models with more compartments, we suggest using higher version of Matlab and R. Matlab works on windows, Mac and Linux Conclusions: New Matlab software codes purposely for numerical simulations of classical deterministic models which can run on any version of Matlab has been introduced in this paper. This code can be edited/modify to suit any deterministic models and any desired output required. An alternative open source free version has been written in R has been provided as well.

A Mathematical Evaluation of the Cost-Effectiveness of Self-Protection, Vaccination, and Disinfectant Spraying for COVID-19 Control

The world is on its path from the post-COVID period, but a fresh wave of the coronavirus infection engulfing most European countries makes the pandemic catastrophic. Mathematical models are of significant importance in unveiling strategies that could stem the spread of the disease. In this paper, a deterministic mathematical model of COVID-19 is studied to characterize a range of feasible control strategies to mitigate the disease. We carried out an analytical investigation of the model’s dynamic behaviour at its equilibria and observed that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number, ${\mathcal{R}}_0$ is less than unity. The endemic equilibrium is also shown to be globally asymptotically stable when ${\mathcal{R}}_0>1$ . Further, we showed that the model exhibits forward bifurcation around ${\mathcal{R}}_0=1$ . Sensitivity analysis was carried out to determine the impact of various factors on the basic reproduction number ${\mathcal{R}}_0$ and consequently, the spread of the disease. An optimal control problem was formulated from the sensitivity analysis. Cost-effectiveness analysis is conducted to determine the most cost-effective strategy that can be adopted to control the spread of COVID-19. The investigation revealed that combining self-protection and environmental control is the most cost-effective control strategy among the enlisted strategies.

Optimal Drug Regimen and Combined Drug Therapy and Its Efficacy in the Treatment of COVID-19: A Within-Host Modeling Study

The COVID-19 pandemic has resulted in more than 524 million cases and 6 million deaths worldwide. Various drug interventions targeting multiple stages of COVID-19 pathogenesis can significantly reduce infection-related mortality. The current within-host mathematical modeling study addresses the optimal drug regimen and efficacy of combination therapies in the treatment of COVID-19. The drugs/interventions considered include Arbidol, Remdesivir, Interferon (INF) and Lopinavir/Ritonavir. It is concluded that these drugs, when administered singly or in combination, reduce the number of infected cells and viral load. Four scenarios dealing with the administration of a single drug, two drugs, three drugs and all four are discussed. In all these scenarios, the optimal drug regimen is proposed based on two methods. In the first method, these medical interventions are modeled as control interventions and a corresponding objective function and optimal control problem are formulated. In this framework, the optimal drug regimen is derived. Later, using the comparative effectiveness method, the optimal drug regimen is derived based on the basic reproduction number and viral load. The average number of infected cells and viral load decreased the most when all four drugs were used together. On the other hand, the average number of susceptible cells decreased the most when Arbidol was administered alone. The basic reproduction number and viral load decreased the most when all four interventions were used together, confirming the previously obtained finding of the optimal control problem. The results of this study can help physicians make decisions about the treatment of the life-threatening COVID-19 infection.

An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect

Currently, the spread of COVID-19 is running at a constant pace. The current situation is not so alarming, but every pandemic has a history of three waves. Two waves have been seen, and now expecting the third wave. Compartmental models are one of the methods that predict the severity of a pandemic. An enhanced SEIR model is expected to predict the new cases of COVID-19. The proposed model has an additional compartment of vaccination. This proposed model is the SEIRV model that predicts the severity of COVID-19 when the population is vaccinated. The proposed model is simulated with three conditions. The first condition is when social distancing is not incorporated, while the second condition is when social distancing is included. The third one condition is when social distancing is combined when the population is vaccinated. The result shows an epidemic growth rate of about 0.06 per day, and the number of infected people doubles every 10.7 days. Still, with imparting social distancing, the proposed model obtained the value of R0 is 1.3. Vaccination of infants and kids will be considered as future work.