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The COVID-19 pandemic is still ongoing, even if the emergency is over, and we now have enough data to analyze the outbreak over a long timeline. There is evidence that the outbreak alternates periods of high and low infections. Retrospectively, this can help in understanding the nature of an appropriate mathematical model for this dramatic infection. The periodic behavior may be the consequence of time-dependent coefficients related to seasonal effects and specific political actions, or an intrinsic feature of the model. The present paper relies on the assumption that the periodic spikes are an intrinsic feature of the disease, and, as such, it should be properly reflected in the mathematical model. Based on the concept of waning immunity proposed for other pathologies, we introduce a new model with (i) a compartment for weakly immune people subject to immunity booster, represented by a non-linear term; (ii) discrimination between individuals infected/vaccinated for the first time, and individuals already infected/vaccinated, undergoing to new infections/doses. We analyze some preliminary properties of our model, called SIRW2, and provide a proof-of-concept that it is capable of reproducing qualitatively the long-term oscillatory behavior of COVID-19 infection. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model to describe the spread of an infectious disease on a farm is developed. To analyze the evolution of the infection, the direct transmission from infected individuals and the indirect transmission from the bacteria accumulated in the enclosure are considered. A threshold value of population is obtained to assure the extinction of the disease. When this size of population is exceeded, two control procedures to apply at each time are proposed. For each of them, a maximum number of steps without control and reducing the prevalence of disease is obtained. In addition, a criterion to choose between both procedures is established. Finally, the results are numerically simulated for a hypothetical outbreak on a farm. [ABSTRACT FROM AUTHOR]

Currently, coronavirus disease 2019 (COVID-19) has become the most severe infectious disease affecting the world, which has spread around the world to more than 200 countries in 2020. Until the number of COVID-19 vaccines is insufficient, nucleic acid testing is considered as an effective way to screen virus carriers and control the spread of the virus. Considering that the medical resources and infection rates are different across various countries and regions, if all infected areas adopt the traditional individual nucleic acid testing method, the workload will be heavy and time-consuming. Therefore, this will not lead to the control of the pandemic. After Wuhan completed a citywide nucleic acid testing in May 2020, China basically controlled the spread of COVID-19 and entered the post-epidemic period. Since then, although some cities in China, such as Qingdao, Xinjiang, Beijing, and Dalian, have experienced a local epidemic resurgence, the pandemic was quickly suppressed through wide-scale pooled nucleic acid testing methods. Combined with the successful experience of mass nucleic acid testing in China, this study introduces two main pooled testing methods used in two cities with a population of more than ten million people, Wuhan's "five-in-one" and Qingdao's "ten-in-one" rapid pooled testing methods. This study proposes an improved method for optimising the second round of "ten-in-one" pooled testing, known as "the pentagram mini-pooled testing method", which speeds up the testing process (as a result of reducing the numbers of testing by 40%) and significantly reduces the cost. Qingdao's optimised "ten-in-one" pooled testing method quickly screens out the infections by running fewer testing samples. This study also mathematically examines the probabilistic principles and applicability conditions for pooled testing of COVID-19. Herein, the study theoretically determines the optimal number of samples that could successfully be combined into a pool under different infection rates. Then, it quantitatively discusses the applicability and principles for choosing the pooled testing instead of individual testing. Overall, this research offers a reference for other countries with different infection rates to help them in implementing the mass testing for COVID-19 to reduce the spread of coronavirus. [ABSTRACT FROM AUTHOR]