Smart Allocation Algorithm for Patient-Therapist Matching (Final Method)

For Therapists (t):

• t_spec: One-hot encoded vector of specializations
• t_exp: Years of experience (normalized)
• t_avail: Availability score (e.g., total available hours per week, normalized)
• t_load: Current patient load (normalized inverse, so higher is better)
• t_rating: Average rating (normalized)

For Patients (p):

• p_diag: One-hot encoded vector of diagnoses
• p_pref: One-hot encoded vector of preferred therapy types
• p_sev: Severity score (normalized)

Similarity Calculation

cosine similarity to calculate how well a therapist matches a patient's needs:

sim(t, p) = cosine_similarity(t_spec, p_diag) * w1 + cosine_similarity(t_spec, p_pref) * w2

w1 and w2 are weights that can be tuned.

Therapist Scoring

For each therapist, calculate a score for a given patient:

score(t, p) = sim(t, p) * (1 + log(t_exp + 1)) * t_avail * (1 - t_load) * t_rating * (1 + log(p_sev + 1))

Allocation Algorithm

For each patient: a. Calculate similarity and initial score for all available therapists b. ML model to get a refined ranking score c. Sort therapists by the ranking score

Continuous Learning

feedback loop where the outcomes of therapist-patient matches (e.g., patient progress, session ratings) are used to continuously train and improve the ML model.

Notation:

Let T be the set of all therapists and P be the set of all patients.

For each t ∈ T and p ∈ P, we want to maximize:

Σ(t,p) ∈ M [ranking_score(t, p)]

subject to:

• ∀t ∈ T: Σ(p:(t,p)∈M) 1 ≤ max_load(t)
• ∀p ∈ P: Σ(t:(t,p)∈M) 1 ≤ 1

*M is the set of matched therapist-patient pairs.