One of the most difficulties that doctors face when diagnosing a disease is making an accurate decision to correctly determine the nature of the injury. This is attributable to the similarity of symptoms for different diseases. The current work is devoted to proposing new mathematical methodologies to help in precise decision-making in the medical diagnosis of the problem of Chikungunya virus disease through the use of soft rough sets. In fact, we introduce some improvements for soft rough sets (given by Feng et al.). We suggest a new approach to studying roughness through the use of soft sets to find approximations of any set, i.e., so-called "soft $\delta$-rough sets". To illustrate this approach, we compare it with the previous studies and prove that the proposed approach is more accurate than the previous works. The proposed approach is more accurate than Feng et al. approach and extends the scope of applications because the problem of soft upper approximation is solved. The main characterizations of the presented technique are elucidated. Some important relations related to soft $\delta$-rough approximations (such as soft $\delta$-memberships, soft $\delta$-equality and soft $\delta$-inclusion) are provided and their properties are examined. In addition, an important medical application in the diagnosis of the problem of Chikungunya virus using soft $\delta$-rough sets is provided with two algorithms. These algorithms were tested on fictitious data in order to compare them to existing methods which represent simple techniques to use in MATLAB. Additionally, we examine the benefits and weaknesses of the proposed approach and present a plan for some upcoming work.