# Improving Healthcare Facilities in Remote Areas Using Cutting-Edge Technologies
## 4 Mathematical Modeling  
This section will evaluate the proposed approach mathematically; our objective function is to optimize healthcare facilities in remote areas under the constraints of limited healthcare facilities. Equation (1) models our objective function  
\[\Theta\text{F}=\text{max}f(\mathcal{T}|[d_{i}])\;s.t\;\partial\in\Omega \tag{1}\]  
where \(f(\mathcal{T}|[d_{i}])\) is the objective function, \(\mathcal{T}\) is the treatment provided to the remote patient, \([d_{i}]\) is the set of decision variables, and \(\Omega\) is the constraint set (or feasible set). Minimize and subject to are shortened to min. and s.t., respectively. The \([d_{i}]\) include four variables as shown in Equation (2):  
\[d_{i}=\left\{\vartheta,\Gamma,S,\vartheta\right\} \tag{2}\]  
\[\text{While }\Omega\in\{\text{I},\mathbb{C},\mathbb{F},\text{A}\} \tag{3}\]  
According to Equation (2), correct vitals, a working telehealth system, accurate patient status, and proper clinical guidelines are the key decision variables to facilitate healthcare facilities in remote areas. Equation (3) describes the constraints that are necessary for optimizing decision variables. These constraints include the proper working of IoT sensors to collect vitals, full-time 5G internet availability to transmit patient vitals to the cloud, and AI algorithms applied to the data fetched through the cloud to get useful information. The remote patient participating in a treatment process according to a clinical guideline \(\vartheta\) often follows a cyclical procedure. In this loop, the patient is in constant contact with his physician. Data on his health are gathered automatically through IoT sensors and uploaded to the cloud, where a treating physician may keep a close eye on things from afar. Different status \(S\) is proposed related to the proper therapy or diagnostic approach depending on the more adequate clinical guideline \(\vartheta\) and the vitals of the patient\(\vartheta\). Depending on the patient's condition and the established therapeutic criteria, a remote physician may alter the course of therapy. Therapy outcomes are affected by a patient's response to the treatment, which might vary based on the patient's disease and other personal factors. These findings will be included as new iteration entries in the subsequent cycle. The therapy in this approach is the conversation system's response to the patient's symptoms. A physician's daily procedure includes iterative analyses of patient data, current status \(S\), and applicable clinical guidelines \(\vartheta\) to bring the patient's condition into compliance with the guidelines. The doctor can change the patient's status if they see fit. That is, using therapy or a diagnostic approach that goes beyond the recommendations of established practice standards. Suppose a doctor thinks the patient's severity is low, while the evidence suggests it is high, for instance. In that case, he may downgrade the patient's status and use the therapies recommended by the clinical guidelines for low severity cases. If he thinks the patient's condition is dire, he may consult an expert panel through the telehealth system. \[\overset{\sim}{\text{S}}=\text{max}_{\vartheta}\rho\left(S\middle|\vartheta,S ^{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text{\text  
According to Equations (6) and (7), clinical guidelines need to be maximized to get proper treatment, which is only possible when the patient's vitals are captured accurately, and the patient's status is best. Furthermore, the previous vitals record is also there, and the telehealth system is working correctly.  
\[\widetilde{\Gamma}=max_{\Gamma}\rho\Big{(}\mathrm{I}|\vartheta,\mathbb{F}, \mathbb{C},S,\vartheta^{\Downarrow}\Big{)} \tag{8}\]  
\[=max_{\Gamma}\rho(\vartheta|I)max_{\Gamma}\rho\Big{(}\mathrm{I}\Big{|}\mathbb{ F},\mathbb{C},S,\vartheta^{\Downarrow}\Big{)} \tag{9}\]  
According to Equations (8) and (9), the telehealth system should be working and available all the time to remote physicians to provide proper treatment.