## 1 Introduction  
Recently, the use of mathematical models in public health decision-making has been increasing, especially to forecast the spread of epidemics [1]. Timely country-based decisions have become critical during the coronavirus disease 2019 (COVID-19) pandemic due to the high contagiousness and the non-negligible proportion of severe cases [2, 3]. After a year of intensive research, several types of vaccines for COVID-19 were developed and approved, but are not widely available in most of the countries [4]. Thus, the use of mathematical models in forecasting the course of this pandemic and the required hospital resources is still relevant in order to enforce measures to maintain the situation at levels that can be sustained by a local health system. A vast amount of works use mathematical models to study the dynamics of the spread of COVID-19 in different contexts [5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. The dynamics of epidemic transmission can be represented by compartmental models based on a system of ordinary differential equations [15]. In these models, the population in a region is divided into groups or compartments such as susceptible, exposed, infectious, recovered, among others, where other groups can be added and/or removed depending on the dynamics or mechanism to be modelled. Among the simplest and most traditional models for the dynamics of transmission of COVID-19, we find the Susceptible-Infectious-Recovered (SIR) model and, the Susceptible-Exposed-Infectious-Recovered (SEIR) model. [PERSON] et al. [5] have presented modifications of the SIR model by considering variable the susceptible population, and [PERSON] [6] have added heterogeneity to the population. Further modifications of the model can be seen in the work of [PERSON] [7], who has included a \"quarantined\" group in order to analyse the effect of isolation of newly confirmed cases. Additionally, [PERSON] et al. [8], based on the SEIR model, proposed to divide the infected group into two groups, being with and without interventions, and have also incorporated the \"quarantined\" and hospitalised groups. On the other hand, [PERSON] and [PERSON] [11] have considered the latently infected and asymptomatic infectious groups in order to take into account the pre-symptomatic or asymptomatic transmission, which are characteristics of the COVID-19 [9; 10]. Additionally, they have subdivided each group into stages to incorporate the Erlang distribution of residence times in each group [16]. There are more elaborate models, such as, SIDARTHE proposed in [12] or \(\theta\)-SEHQRD presented in [13], where more compartments are included. In metapopulation models, the spread dynamic of disease is split into age groups or regions, and these groups are interconnected to each other by additional interaction or mobility terms. For instance, [PERSON] et al. [14] applied a metapopulation model with age-stratified and mobility-based for the spread of COVID-19. Although there have been published several works proposing mathematical models for the spread dynamics of COVID-19, there are still challenges in adapting particular models in specific situations. These challenges are related to:  
* the amount of available data and the quality of such data, that vary from one country to another, and
* the containment strategies applied in each country. In particular, highly detailed models are composed of many parameters, which have to be determined independently, using different groups of data. When the available data is limited, then the models with many parameters are over-fitted, which increases the prediction error [17]. However, the simple SIR or SEIR models with constant parameters along the epidemic cycle, fail to represent the dynamics when different containment strategies are applied along the time. Thus, we developed a mathematical model, which is as simple as possible, but at the same time, applicable to several situations. Our model, named SEIR-H, is based on the simple SEIR model, where R stands for reported instead of recovered.