Table 5.

Various epidemiological models for different infectious diseases.

S. no.	References	Conclusion drawn
1	Huppert and Katriel (84)	The authors have discussed the extent to which the disease transmission models provide reliable predictions. They examined the predictions of the model to test which are trustworthy. An important benefit derived from mathematical modeling activity is that it demands transparency and accuracy regarding our assumptions, thus enabling us to test our understanding of the disease epidemiology by comparing model results and observed patterns. Models can also assist in decision-making by making projections regarding important issues such as intervention-induced changes in the spread of disease.
2	Steele et al. (85)	The authors mentioned that the early detection of infectious disease outbreaks can reduce the ultimate size of the outbreak, with lower overall morbidity and mortality due to the disease. In the review, they have mentioned numerous approaches to the earlier detection of outbreaks exist. In the systematic review the authors used of PRISMA framework (Preferred Reporting Items for Systematic Reviews and Meta-analyses), The MEDLINE (PubMed) database. Five studies were identified and included in the review. These studies evaluated the effect of electronic-based reporting on detection timeliness, the impact of laboratory agreements on timeliness, and barriers to notification by general practitioners.
3	Driessche (86)	The author worked on the basic reproduction number, R0, for infectious diseases, and other reproduction numbers related to R0 that are useful in guiding control strategies. Beginning with a simple population model, the concept is developed for a threshold value of R0 determining whether or not the disease dies out. The next generation matrix method of calculating R0 in a compartmental model is described and illustrated. These theoretical ideas are then applied to models that are formulated for West Nile virus in birds (a vector-borne disease), cholera in humans (a disease with two transmission pathways), anthrax in animals (a disease that can be spread by dead carcasses and spores), and Zika in humans (spread by mosquitoes and sexual contacts). Finally, references for other ways to calculate R0 are given and these are useful for more complicated models.
4	Walters et al. (87)	The authors observed that mathematical models can aid in the understanding of the risks associated with the global spread of infectious diseases. To assess the current state of mathematical models for the global spread of infectious diseases, the authors reviewed the literature highlighting common approaches and good practice, and identifying research gaps. They found that most epidemiological data come from published journal articles, population data come from a wide range of sources, and travel data mainly come from statistics or surveys, or commercial datasets. However, they believed that open access datasets should be used wherever possible to aid model reproducibility and transparency.
5	Raissi et al. (88)	The authors considered the compartmental disease transmission models and discuss the importance of determining model parameters that provide an insight into disease transmission and prevalence. They used three approaches including an optimization approach, a physics informed deep learning, and a statistical inference method to estimate parameters and analyze disease transmission. The performance of the deep learning method is validated against representative small and big data sets corresponding to a well-known benchmark example and the results indicate that deep learning is a viable candidate to determine model parameters. The results indicate the efficiency and importance of statistical inference methods for researchers to understand and analyze the data to make confident predictions.
6	Li et al. (36)	The authors established the dynamics model of infectious diseases and the time series model to predict the trend and short-term prediction of the transmission of COVID-19, in mainland China for clinical trials. They applied the dynamic models of the six chambers and established the time series models based on different mathematical formulas according to the variation law of the original data. Finally, they suggested that it is a very effective prevention and treatment method to continue to increase investment in various medical resources to ensure that suspected patients can be diagnosed and treated promptly.
7	Prasse et al. (89)	The authors have used a network-based model to describe the COVID-19 epidemic in the Hubei province. They have suggested the network-inference-based prediction algorithm (NIPA) to predict the future prevalence of the COVID-19 epidemic in the cities of China and they have shown that NIPA is best for accurate prediction of the infection spread.
8	Yang et al. (90)	The authors have described the short-term predictor of the daily cases reported in Wuhan City using individual-level network-based model to rebuilt the epidemic dynamics in Hubei Province and have seen the effectiveness of non-pharmaceutical interventions on the epidemic spreading with various scenarios. They have shown through the simulation study that without continued control measures, the epidemic in Hubei Province could have become persistent and the infection rate is controlled through protective measures and social distancing. They have demonstrated the COVID-19 transmission with non-Markovian processes and have shown how these models produce different epidemic trajectories, in comparison to Markov processes.
9	Popov and Nakov (91)	The authors worked on the epidemiological models of the spread of infectious diseases, including COVID-19. The models and simulations of an epidemic in the presence of quarantine and the moment of its termination have been made. They have pointed out that it is important to pinpoint the timing of the lifting of measures or their granting. They have shown through the proposed simulation model that the impact of group gatherings such as the beginning of the school year, holidays, and more, mass events on the epidemic picture. These studies are also relevant in the event of a mutation in the virus that will change the rate of spread.
10	Saraee and Silva (92)	In this review, the authors have compared studies that have used epidemiological models for disease forecasting and other models that have identified socio-demographic factors associated with COVID-19. They have evaluated several models, from basic equation-based mathematical models to more advanced machine-learning ones. They have identified high-impact models used by policymakers and discussing their limitations, They have suggested possible areas of applications for future research.
10	Moein et al. (93)	The authors have used different mathematical techniques, including the susceptible-infected-recovered (SIR) model for the description and prediction of the infection spread of COVID-19. They have simulated the infection spread data in Isfahan province of Iran along with three suppressive measures of the stringency level of physical distancing. They have shown that for the short term prediction, SIR model was only able to predict the actual spread and pattern of COVID-19 while not in long term. They have also concluded that other published works using SIR models for predicting COVID-19 has the same drawback. The assumptions for SIR models are not true for COVID-19 pandemic. Finally they have suggested that more sophisticated modeling strategies and detailed knowledge of the biomedical and epidemiological aspects of the disease are needed to predict the spread of this pandemic.
11	Alvarez et al. (94)	The authors come up with a simple epidemiological model which may be implemented in Excel spreadsheets and able to simulate the data of the COVID-19 pandemic significantly. They have shown that the model may closely follow the evolution of COVID-19 spread in big cities by simply adjusting parameters of demographic conditions and aggressiveness of the response to epidemics. Further they have also advised that the suggested epidemiological simulator may be used to judge the efficiency of the response of population to the pandemic. The simplicity and accuracy of the model will help to understand the extent of an epidemic event and the efficacy of any policy response from the state.