Effects of heterogeneous susceptibility on epidemiological models of reinfection.

This paper studies an epidemic model with heterogeneous susceptibility which generalizes the SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered) and SIRI (susceptible-infected-recovered-infected) models. The proposed model considers the case that some infected people are susceptible again after recovery, some infected people develop immunity after infection, and some infected people are reinfected after recovery. We perform a comprehensive theoretical analysis of the model, showing that under appropriate initial conditions, delayed outbreak phenomenon occurs that can give people false impressions. Moreover, compared with the SIRI model, the proposed model exists the delayed outbreak phenomenon under more probable conditions. Finally, we present a numerical example to illustrate the effectiveness of the theoretical results.

Vaccination control of an epidemic model with time delay and its application to COVID-19.

This paper studies an SEIR-type epidemic model with time delay and vaccination control. The vaccination control is applied when the basic reproduction number R 0 > 1 . The vaccination strategy is expressed as a state delayed feedback which is related to the current and previous state of the epidemic model, and makes the model become a linear system in new coordinates. For the presence and absence of vaccination control, we investigate the nonnegativity and boundedness of the model, respectively. We obtain some sufficient conditions for the eigenvalues of the linear system such that the nonnegativity of the epidemic model can be guaranteed when the vaccination strategy is applied. In addition, we study the stability of disease-free equilibrium when R 0 < 1 and the persistent of disease when R 0 > 1 . Finally, we use the obtained theoretical results to simulate the vaccination strategy to control the spread of COVID-19.

Control of a multigroup COVID-19 model with immunity: treatment and test elimination.

This paper introduces a multigroup COVID-19 model with immunity, in which the total population of each group is partitioned into five compartments, that is, susceptible, exposed, infective, infective in treatment and recovered compartment. If the basic reproduction number is less than or equal to one, and the infection graph is strongly connected, then the disease-free equilibrium is globally asymptotically stable and the disease dies out. However, the COVID-19 is already in a pandemic state, and the basic reproduction number is large than one. Hence, in order to make the COVID-19 die out in some groups in an area, we design some appropriate control strategies which reduce the number of exposed people and increase the number of people treated. These two methods have been proved to be the most effective methods at present. An effective algorithm is proposed to identify the groups that need to be controlled. Finally, we use the actual limited data of Hubei, Guangdong and Zhejiang provinces in China to illustrate the effectiveness of the obtained results.