In this paper, a reaction-diffusion SIR epidemic model is proposed. It takes into account the individuals mobility, the time periodicity of the infection rate and recovery rate, and the general nonlinear incidence function, which contains a number of classical incidence functions. In our model, due to the introduction of the general nonlinear incidence function, the boundedness of the infected individuals can not be obtained, so we study the existence and nonexistence of periodic traveling wave solutions of original system with the aid of auxiliary system. The basic reproduction number R 0 and the critical wave speed c * are given. We obtained the existence and uniqueness of periodic traveling waves for each wave speed c > c * using the Schauder's fixed points theorem when R 0 > 1 . The nonexistence of periodic traveling waves for two cases (i) R 0 > 1 and 0 less then c less then c * , (ii) R 0 ≤ 1 and c ≥ 0 are also obtained. These results generalize and improve the existing conclusions. Finally, the numerical experiments support the theoretical results. The differences of traveling wave solution between periodic system and general aperiodic coefficient system are analyzed by numerical simulations.In this paper a fractional optimal control problem was formulated for the outbreak of COVID-19 using a mathematical model with fractional order derivative in the Caputo sense.  https://www.selleckchem.com/products/ak-7.html  The state and co-state equations were given and the best strategy to significantly reduce the spread of COVID-19 infections was found by introducing two time-dependent control measures, u 1 ( t ) (which represents the awareness campaign, lockdown, and all other measures that reduce the possibility of contacting the disease in susceptible human population) and u 2 ( t ) (which represents quarantine, monitoring and treatment of infected humans). Numerical simulations were carried out using RK-4 to show the significance of the control functions. The exposed population in susceptible population is reduced by the factor ( 1 - u 1 ( t ) ) due to the awareness and all other measures taken. Likewise, the infected population is reduced by a factor of ( 1 - u 2 ( t ) ) due to the monitoring and treatment by health professionals.Considering the great effect of vaccination and the unpredictability of environmental variations in nature, a stochastic Susceptible-Vaccinated-Infected-Susceptible (SVIS) epidemic model with standard incidence and vaccination strategies is the focus of the present study. By constructing a series of appropriate Lyapunov functions, the sufficient criterion R 0 s > 1 is obtained for the existence and uniqueness of the ergodic stationary distribution of the model. In epidemiology, the existence of a stationary distribution indicates that the disease will be persistent in a long term. By taking the stochasticity into account, a quasi-endemic equilibrium related to the endemic equilibrium of the deterministic system is defined. By means of the method developed in solving the general three-dimensional Fokker-Planck equation, the exact expression of the probability density function of the stochastic model around the quasi-endemic equilibrium is derived, which is the key aim of the present paper. In statistical significance, the explicit density function can reflect all dynamical properties of an epidemic system. Next, a simple result of disease extinction is obtained. In addition, several numerical simulations and parameter analyses are performed to illustrate the theoretical results. Finally, the corresponding results and conclusions are discussed at the end of the paper.A SEIR-type model is investigated to evaluate the effects of awareness campaigns in the presence of factors that can induce overexposure to disease. We find that high levels of overexposure can drive system dynamics towards a backward phenomenology and that increasing people awareness through balanced and aware information can be crucial to avoid dangerous dynamical transitions as hysteresis or transient oscillations before disease eradication. Investigations in the time dependent regimes are provided to support the results. Google Trends data in the context of Covid19 are also used to stress how low levels of awareness, combined with high overexposure, can be related to recent episodes of epidemic resurgence in Europe. Our results suggest that the interplay between overexposure and awareness is a point that should not be underestimated both in the current and future management of the Covid19 emergency.This paper explores how individuals-defined along lines of gender, age, life experience, financial capital and profession-experience and react in nuanced ways to the impacts of state-led COVID-19 measures, in Sierra Leone. The findings are based on ethnographic data collected from Makeni city and three rural communities in Bombali District, north Sierra Leone during the outbreak of COVID-19, between 23rd March and 6th May 2020. The findings show how state-led measures-indefinite district lockdown, three-day total lockdowns and mask wearing-were experienced and responded to in myriad ways, including adapting, not complying and resisting. The diverse ways members of society experience, react and shape the effects of internationally and nationally informed health policies during a global pandemic in Sierra Leone highlight the nuances of individual experience and agency in specific socio-political contexts. These findings contribute to the emerging Social Science debate on state-society relations in the COVID-19 pandemic response.This paper presents models of the spread of SARS-CoV-2 coronavirus in individual countries and globally in 2020 based on the statistical characteristics of the spread in the given countries or regions (in particular, in Hubei province). Through modeling, we attempt to achieve a goal which is of vital interest to societies in a pandemic catastrophe, and to answer the question of what stage of spread the epidemic has reached in a given country. The country classifier we developed is based on the relative variability indicator of the confirmed cases variable. This classification indicator is compared with a set of data-driven thresholds, the crossing of which determines the degree of spread of the epidemic in a given country. The article was written between April 2020, when the pandemic had been suppressed in China and was raging in Europe and the USA, and August 2020, as a new wave of local resumed outbreaks appeared in many countries. We contend that the spread phases are predictable based on statistical similarity.