Modeling the effects of prosocial awareness on COVID-19 dynamics: Case studies on Colombia and India

Optimal control analysis on the spread of COVID-19: Impact of contact transmission and environmental contamination

The study investigates the intricate dynamics of SARS-CoV-2 transmission, with a particular focus on both close-contact interactions and environmental factors. Using advanced mathematical modeling and epidemiological analysis, explored the effects of these transmission pathways on the spread of COVID-19. The equilibrium points for both disease-free and endemic states are calculated and evaluated to determine their global stability. Additionally, the basic reproduction number (R0) is derived to quantify the transmission potential of the virus. To ensure model accuracy, numerical simulations are performed using MATLAB, utilizing daily COVID-19 case data from India. Parameter values are sourced from existing literature, with certain parameters estimated through fitting the model to observed data. Crucially, the model incorporates environmental transmission factors, such as surface contamination and airborne spread. The inclusion of these factors provides a more comprehensive understanding of the virus's spread, demonstrating the importance of interventions like use of face masks, environmental sanitization, vaccine efficacy, availability of treatment resources underappreciated when focusing solely on direct human contact. A sensitivity analysis is conducted to assess the impact of different parameters on R0, with results visualized through heat maps to identify the most influential factors. Furthermore, Pontryagin's maximum principle is employed to develop an optimal control model, enabling the formulation of effective intervention strategies. By analysing both interpersonal and environmental transmission mechanisms, this study offers a more holistic framework for understanding SARS-CoV-2 transmission. The insights gained are critical for informing public health strategies, emphasizing the necessity of addressing both direct contact and environmental sources of infection to more effectively manage current and future outbreaks.

Human movement avoidance decisions during Coronavirus disease 2019 in Japan

Understanding host behavioral change in response to epidemics is important to forecast the disease dynamics. To predict the behavioral change relevant to the epidemic situation (e.g., the number of reported cases), we need to know the epidemic situation at the moment of decision, which is difficult to identify from the records of actually performed human mobility. In this study, the largest travel accommodation reservation data covering half of the existed accommodations in Japan was analyzed to observe decision-making timings and how it responded to the changing epidemic situation during Japan's Coronavirus Disease 2019 until February 2023. To this end, we measured mobility avoidance index proposed in Ito et al., 2022 to indicate people's decision of mobility avoidance and quantified it using the time-series of the accommodation booking/cancellation data. We observed matches of the peak dates of the mobility avoidance and the number of reported cases, and mobility avoidance changed proportional to the logarithmic number of reported cases. We also found that the slope of mobility avoidance against the change of the logarithmic number of reported cases were similar among the epidemic waves, while the intercept of that was much reduced as the first epidemic wave passed by. People measure the intensity of epidemic by logarithm of the number of reported cases. The sensitivity of their response is established during the first wave and the people's response became weakened after the first experience, as if the number of reported cases were multiplied by a constant small factor.

Waves of infection emerging from coupled social and epidemiological dynamics

The coronavirus (SARS-CoV-2) exhibited waves of infection in 2020 and 2021 in Japan. The number of infected had multiple distinct peaks at intervals of several months. One possible process causing these waves of infection is people switching their activities in response to the prevalence of infection. In this paper, we present a simple model for the coupling of social and epidemiological dynamics. The assumptions are as follows. Each person switches between active and restrained states. Active people move more often to crowded areas, interact with each other, and suffer a higher rate of infection than people in the restrained state. The rate of transition from restrained to active states is enhanced by the fraction of currently active people (conformity), whereas the rate of backward transition is enhanced by the abundance of infected people (risk avoidance). The model may show transient or sustained oscillations, initial-condition dependence, and various bifurcations. The infection is maintained at a low level if the recovery rate is between the maximum and minimum levels of the force of infection. In addition, waves of infection may emerge instead of converging to the stationary abundance of infected people if both conformity and risk avoidance of people are strong.

Modeling and Analysis of COVID-19 Spread: The Impacts of Nonpharmaceutical Protocols

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 and endemic equilibrium points in terms of the basic reproduction number, is presented. The sensitivity analysis indicates that reducing the disease contact rate and the transmissibility factor related to asymptomatic individuals, along with increasing the quarantine/self-isolation rate and the contact-tracing process, from the view of flattening the curve for novel coronavirus, are crucial to the reduction in disease-related deaths.

Mathematical modeling of COVID-19 pandemic in the context of sub-Saharan Africa: a short-term forecasting in Cameroon and Gabon

In this paper, we propose and analyse a compartmental model of COVID-19 to predict and control the outbreak. We first formulate a comprehensive mathematical model for the dynamical transmission of COVID-19 in the context of sub-Saharan Africa. We provide the basic properties of the model and compute the basic reproduction number $\mathcal {R}_0$ when the parameter values are constant. After, assuming continuous measurement of the weekly number of newly COVID-19 detected cases, newly deceased individuals and newly recovered individuals, the Ensemble of Kalman filter (EnKf) approach is used to estimate the unmeasured variables and unknown parameters, which are assumed to be time-dependent using real data of COVID-19. We calibrated the proposed model to fit the weekly data in Cameroon and Gabon before, during and after the lockdown. We present the forecasts of the current pandemic in these countries using the estimated parameter values and the estimated variables as initial conditions. During the estimation period, our findings suggest that $\mathcal {R}_0 \approx 1.8377 $ in Cameroon, while $\mathcal {R}_0 \approx 1.0379$ in Gabon meaning that the disease will not die out without any control measures in theses countries. Also, the number of undetected cases remains high in both countries, which could be the source of the new wave of COVID-19 pandemic. Short-term predictions firstly show that one can use the EnKf to predict the COVID-19 in Sub-Saharan Africa and that the second vague of the COVID-19 pandemic will still increase in the future in Gabon and in Cameroon. A comparison between the basic reproduction number from human individuals $\mathcal {R}_{0h}$ and from the SARS-CoV-2 in the environment $\mathcal {R}_{0v}$ has been done in Cameroon and Gabon. A comparative study during the estimation period shows that the transmissions from the free SARS-CoV-2 in the environment is greater than that from the infected individuals in Cameroon with $\mathcal {R}_{0h}$ = 0.05721 and $\mathcal {R}_{0v}$ = 1.78051. This imply that Cameroonian apply distancing measures between individual more than with the free SARS-CoV-2 in the environment. But, the opposite is observed in Gabon with $\mathcal {R}_{0h}$ = 0.63899 and $\mathcal {R}_{0v}$ = 0.39894. So, it is important to increase the awareness campaigns to reduce contacts from individual to individual in Gabon. However, long-term predictions reveal that the COVID-19 detected cases will play an important role in the spread of the disease. Further, we found that there is a necessity to increase timely the surveillance by using an awareness program and a detection process, and the eradication of the pandemic is highly dependent on the control measures taken by each government.

SARS-coronavirus-2 infections: biological instabilities characterized by order parameters

A four-variable virus dynamics TIIV model was considered that involves infected cells in an eclipse phase. The state space description of the model was transferred into an amplitude space description which is the appropriate general, nonlinear physics framework to describe instabilities. In this context, the unstable eigenvector or order parameter of the model was determined. Subsequently, a model-based analysis of viral load data from eight symptomatic COVID-19 patients was conducted. For all patients, it was found that the initial SARS-CoV-2 infection evolved along the respective patient-specific order parameter, as expected by theoretical considerations. The order parameter amplitude that described the initial virus multiplication showed doubling times between 30 minutes and 3 hours. Peak viral loads of patients were linearly related to the amplitudes of the patient order parameters. Finally, it was found that the patient order parameters determined qualitatively and quantitatively the relationships between the increases in virus-producing infected cells and infected cells in the eclipse phase. Overall, the study echoes the 40 years old suggestion by Mackey and Glass to consider diseases as instabilities.

A mechanistic model for airborne and direct human-to-human transmission of COVID-19: effect of mitigation strategies and immigration of infectious persons

The COVID-19 pandemic is the most significant global crisis since World War II that affected almost all the countries of our planet. To control the COVID-19 pandemic outbreak, it is necessary to understand how the virus is transmitted to a susceptible individual and eventually spread in the community. The primary transmission pathway of COVID-19 is human-to-human transmission through infectious droplets. However, a recent study by Greenhalgh et al. (Lancet 397:1603-1605, 2021) demonstrates 10 scientific reasons behind the airborne transmission of SARS-COV-2. In the present study, we introduce a novel mathematical model of COVID-19 that considers the transmission of free viruses in the air beside the transmission of direct contact with an infected person. The basic reproduction number of the epidemic model is calculated using the next-generation operator method and observed that it depends on both the transmission rate of direct contact and free virus contact. The local and global stability of disease-free equilibrium (DFE) is well established. Analytically it is found that there is a forward bifurcation between the DFE and an endemic equilibrium using central manifold theory. Next, we used the nonlinear least-squares technique to identify the best-fitted parameter values in the model from the observed COVID-19 mortality data of two major districts of India. Using estimated parameters for Bangalore urban and Chennai, different control scenarios for mitigation of the disease are investigated. Results indicate that the vaccination of susceptible individuals and treatment of hospitalized patients are very crucial to curtailing the disease in the two locations. It is also found that when a vaccine crisis is there, the public health authorities should prefer to vaccinate the susceptible people compared to the recovered persons who are now healthy. Along with face mask use, treatment of hospitalized patients, and vaccination of susceptibles, immigration should be allowed in a supervised manner so that economy of the overall society remains healthy.

The modeling and analysis of the COVID-19 pandemic with vaccination and treatment control: a case study of Maharashtra, Delhi, Uttarakhand, Sikkim, and Russia in the light of pharmaceutical and non-pharmaceutical approaches

Nonlinear dynamics is an exciting approach to describe the dynamical practices of COVID-19 disease. Mathematical modeling is a necessary method for investigating the dynamics of epidemic diseases. In the current article, an effort has been made to cultivate a novel COVID-19 compartment mathematical model by incorporating vaccinated populations. Primarily, the fundamental characteristics of the model, such as positivity and boundedness of solutions, are established. Thereafter, equilibrium analysis of steady states has been illustrated through vaccine reproduction number. Further, a nonlinear least square curve fitting technique has been employed to recognize the best fitted model parameters from the COVID-19 mortality data of five regions, namely Maharashtra, Delhi, Uttarakhand, Sikkim, and Russia. The numerical framework of the model has been added to interpret the consequence of various control schemes (pharmaceutical or non-pharmaceutical) on COVID-19 dynamics, and it has been ascertained that all the control protocols have a positive influence on curtailing the COVID-19 transference in the aforementioned regions. In addition, the essence of vaccine efficacy and vaccine-induced immunity are examined by considering different scenarios. Our analysis demonstrates that the disease will be wiped off from the Maharashtra, Delhi, Uttarakhand and Sikkim regions of India, while it shall persist in Russia for some more time. It is also found that, if a vaccine calamity arises, the government should majorly focus on permanent drug treatment of hospitalized individuals rather than vaccination.

Protect ya Grandma! The Effects of Students' Epistemic Beliefs and Prosocial Values on COVID-19 Vaccination Intentions

The present study investigates epistemic beliefs (beliefs about the nature of knowledge and knowing) and prosocial values as predictors of COVID-19 vaccination intentions. As a first hypothesis, we posit that beliefs in justification by authority will positively relate to vaccination intentions. Second, we expect a positive relationship between prosocial values and vaccination intentions. Third, we hypothesize that beliefs in justification by authority moderate the relationship between prosocial values and vaccination intentions, so that the positive correlation between prosocial values and vaccination intentions becomes stronger with increasing beliefs in justification by authority. Hypotheses were tested in a sample of N = 314 German university students, a group with rather high mobility, who, when vaccinated, will increase the chance of attaining herd immunity. Hypotheses were tested using correlational and multiple regression analyses. Results revealed a highly significant positive relationship between justification by authority and vaccination intentions, whereas both hypotheses that included prosocial values did not yield significant results. Additional exploratory analyses revealed that the relationship between justification by authority and vaccination intentions was mediated by beliefs in the safety and effectiveness of the vaccines. Furthermore, significant negative relationships were found between personal justification and vaccination intentions as well as between justification by multiple sources and vaccination intentions. These results highlight the crucial role of science and public health communication in fostering vaccination intentions regarding COVID-19.

Rise and Decay of the COVID-19 Epidemics in the USA and the State of New York in the First Half of 2020: A Nonlinear Physics Perspective Yielding Novel Insights

As of December 2020, since the beginning of the year 2020, the COVID-19 pandemic has claimed worldwide more than 1 million lives and has changed human life in unprecedented ways. Despite the fact that the pandemic is far from over, several countries managed at least temporarily to make their first-wave COVID-19 epidemics to subside to relatively low levels. Combining an epidemiological compartment model and a stability analysis as used in nonlinear physics and synergetics, it is shown how the first-wave epidemics in the state of New York and nationwide in the USA developed through three stages during the first half of the year 2020. These three stages are the outbreak stage, the linear stage, and the subsiding stage. Evidence is given that the COVID-19 outbreaks in these two regions were due to instabilities of the COVID-19 free states of the corresponding infection dynamical systems. It is shown that from stage 1 to stage 3, these instabilities were removed, presumably due to intervention measures, in the sense that the COVID-19 free states were stabilized in the months of May and June in both regions. In this context, stability parameters and key directions are identified that characterize the infection dynamics in the outbreak and subsiding stages. Importantly, it is shown that the directions in combination with the sign-switching of the stability parameters can explain the observed rise and decay of the epidemics in the state of New York and the USA. The nonlinear physics perspective provides a framework to obtain insights into the nature of the COVID-19 dynamics during outbreak and subsiding stages and allows to discuss possible impacts of intervention measures. For example, the directions can be used to determine how different populations (e.g., exposed versus symptomatic individuals) vary in size relative to each other during the course of an epidemic. Moreover, the timeline of the computationally obtained stages can be compared with the history of the implementation of intervention measures to discuss the effectivity of such measures.