Developing an SEIHR epidemiological model featuring saturated incidence rate and investigating its stability

Each and every person will inevitably come into contact with infectious diseases over their lifetime. This unavoidable phenomena is a characteristic of all people. Ideally, the effects of such diseases are still controllable, but under unfavourable circumstances, they may worsen and become full-fledged outbreaks. As a result, this article tries to offer an SEIHR model whose main goal is to reduce and stop the transmission of infectious diseases. Notably, infectious diseases continue to plague many countries, represented by the global threat of Covid-19, underlining the urgent need for efficient control methods. This model stands out because it carefully takes into account the saturated incidence rate of infectivity. The concept also divides the infected population into two different groups, enabling more focused and customized medical interventions. The article begins by closely examining the positivity and boundedness of the model, then conducts a thorough analysis of the fundamental reproductive number. The model's stability is then categorically proven at both equilibrium points. In summary, the article concludes with convincing numerical simulations that validate the suggested model, providing convincing evidence of its effectiveness as a whole. In conclusion, the suggested SEIHR model, which is supported by a wealth of empirical evidence confirming its efficacy and optimality, represents a significant advancement in the management and containment of infectious diseases. It offers a promising route for addressing the enduring threat of infectious diseases on a global scale, and its unique form and extensive analysis highlight its potential to alter our approach to infectious disease control.