625.651.8VL - Mathematical Models in Healthcare

Applied and Computational Mathematics
Summer 2022


A firm mathematical foundation for work in biostatistics is provided by a detailed consideration of four mathematical frameworks that can be applied throughout medicine. The class will focus on these framework ideas, which build on earlier coursework in statistics and probability, and their applications. The mathematical frameworks are Markov models, Gaussian processes, logistic regression, and Bayesian networks. The clinical settings to be explored will be associated with treatment, prognosis, and survival within the settings of asthma, diabetes, cancer, and epidemics. While the course is primarily mathematical, students will be expected to work within at least one programming environment (R or Python will be easiest, but Julia, MATLAB, and others will also be supported).


Profile photo of Thomas Woolf.

Thomas Woolf


Course Structure

The course materials are divided into modules which can be accessed by clicking Modules on the course menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Please note that since we are a Virtual Live (VL) class the Modules will populate as we go into each week's lecture time.

Course Topics

These four mathematical approaches to problems in healthcare will be covered in the context of both class-time, break-out room problems, and within your class projects.  The goal is to learn at least one of these methods in detail and to feel comfortable with the other three. These methods go beyond their applications within healthcare, so you should find all of these methods to be generally helpful regardless of whether you are primarily interested in healthcare or have your main interests outside of healthcare.

Course Goals

Our major goal is to develop skills and understanding around the challenges of making models for healthcare.  This means that the course should enable you to understand, with detail, how EHR data is structured, how models can be made from that data, and what challenges arise within each type of model.

Course Learning Outcomes (CLOs)


All four textbooks are available as electronic downloads from the JHU library:

Markov Models:

  Hidden Markov Models for Time Series, An Introduction using R,  Zucchini, MacDonald, and Langrock

Gaussian Processes:

  Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences, Gramacy, CRC Press

Logistic Regression:

  Regression Methods in Biostatistics, Vittinghoff, Glidden, Shiboski, and McCulloch, Springer

Bayesian Networks:

  Risk Assessment and Decision Analysis with Bayesian Networks, Fenton and Neil, CRC Press

Student Coursework Requirements

Student Coursework Requirements: 


  • Weekly problem sets (25% of final grade)   
  • Breakout room problems (25% of final grade) 
  • Term project with interim deliverables throughout semester (50%) - Full introduction in module 1.
    • Project concept and Choices 
    • Module 2 - Submit initial ideas  (5%) 
    • Module 7 - Pseudo code and outline (5%) 
    • Module 8 – Bibliography (10%) 
    • Module 10 - Connections & Methods (20%) 
    • Module 12 – Final Project Submission (60%) 

Grading Policy

EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).

Score RangeLetter Grade
100-97= A+
96-93= A
92-90= A−
89-87= B+
86-83= B
82-80= B−
79-77= C+
76-73= C
72-70= C−
69-67= D+
66-63= D
<63= F

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.