ASIAN JOURNAL OF MATHEMATICS AND APPLICATIONS Volume 2021, Article ID ama0568, 13 pages ISSN 2307-7743 http://scienceasia.asia MATHEMATICAL MODELING OF COVID-19 AND ITS TRANSMISSION IN CASE OF ETHIOPIA ZELEKE BEZA * , GEMECHU DIRIBA Mathematics Department, Mettu University, Mettu, Ethiopia * Correspondence: bezeleke48@yahoo.com Abstract. In this paper, we attempt to describe the spread of COVID-19 based on an extensions of the well-known SEIR models. We bring in a new representation to appraise and manage the spread of infectious disease COVID-19 through SEIHR pandemic model, which is based on the supposition that the infected individuals are isolated and the necessary treatments are arranged so that they cannot taint the other residents in the community. Dynamics of the SEIHR model is presented by basic reproduction number R 0 and the comprehensive stability analysis. The reproduction number was also determined for the epidemiological model and found to be consistent with the local stability condition for the disease-free equilibrium. We establish the positivity and boundedness of solutions, local and global stability analysis of equilibria to examine its epidemiological relevance. To validate the model and estimating the important model parameters and prediction about the disease, we consider the real cases of Ethiopia from 4th March to 20th August 2020. 1. Introduction In December 2019, corona virus first reported in Wuhan, China, is an infectious disease caused by a newly discovered corona virus. The virus is now known as the severe acute respiratory syndrome corona virus 2 (SARS-CoV-2). The disease it causes is called corona virus disease 2019 (COVID-19) [1]. According to WHO Novel Corona virus disease situa- tion report 21 January 2020, the first case outside of China was reported in Thailand on 13 January 2020, Japan on 15 January 2020 and Republic of Korea on 20 January 2020 [2]. Currently the COVID-19 outbreak has now spread over the world. According to WHO the symptoms of COVID-19 may appear two to 14 days after exposure. This time after exposure and before having symptoms is called the incubation period i.e., during this period the infected humans are not infectious. However, the patients infected by COVID-19 will have symptoms including fever, cough and difficulty breathing, and the severe patients may have renal failure. This list is not all inclusive [3]. Current evidence suggests that COVID-19 Key words and phrases. Mathematical Modeling, COVID-19, Ethiopia. ©2021 Science Asia 1