#### Assistant Professor

Department of Electrical Engineering

#### Biography

Muhammad Rafiq has been working as assistant professor at UCP for 11.5 years. His areas of specialization are Applied Mathematics, Numerical Modeling and Mathematical Biology. He has work experience of 12 years.

#### Courses At UCP

• Applied Calculus
• Numerical Analysis

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#### Research

Research Projects

1. Numerical Analysis of Delayed Epidemic Models

Description:
The mechanism of a disease spread can be studied by modelling the transmission dynamics infectious diseases. The future course of an outbreak and measures to control an epidemic can be predicted through modelling. The basic idea of modelling to study the rapid rise and fall of infected population was given by W. Kermik and A. McKendrik, in 1927.In this project, a modified delayed SIR epidemic model with susceptibility effect has been constructed by keeping in mind the vital dynamics and constant population size as proposed by Hethcote in 1976.The aim of this project is to develop and analyze reliable numerical techniques to study the effect of time delay on the transmission dynamics of an infectious disease.
2. Spatio-Temporal Numerical Modeling of Infectious Diseases Dynamics
Collaborators: Dr. Aziaz-u-Rehman , Muhammad Nouman
Description:
Partial differential equation (PDE) models of infectious diseases are more realistic in nature. These models are used to investigate the spatio-temporal behavior of an epidemic in a population.  In this project, we shall discuss the transmission dynamics of infectious diseases using partial differential equations. The goal of this project is to perform reliable numerical analysis for the spatio-temporal dynamics of infectious diseases.
3. Optimal Control for Stochastic Model of Epidemic Infections
Students: Huma Rehman
Description:
Goal of this Project is to develop optimal control policy that can answer the questions such as: when to use vaccination, when to treat the infected individuals, when to use quarantine for preventing the spread of the infection etc. For this purpose, the dynamic model of the epidemic infection has been used for analysis and design of the optimal control policy.

#### List of Publications

Journal Publications:

1. Zain Ul Abadin Zafar, Kashif Rehan, M. Mushtaq, Rafiq. “Numerical Treatment for Nonlinear Brusselator Chemical Model”. Journal of difference Equations and Applications (2016). http://dx.doi.org/10.1080/10236198.2016.1257005
2. Zain Ul Abadin Zafar, Anjum Pervaiz, Rafiq,M. O. Ahmad,. “Fourth Order Compact Method for One Dimensional Heat Equation”Pak.J.Engg. &Appl.Sci.Vol. 19, p.45-50. (2016)
3. Zain Ul Abadin Zafar, Anjum Pervaiz, M. O. Ahmad, Rafiq. “Fourth Order Compact Method for One Dimensional Inhomogeneous Telegraph Equation with”. Pak.J.Engg. &Appl.Sci.Vol. 19, p.77-82.(2016)
4. Rafiq, M.O. Ahmad, “Non-Standard Finite Difference Modeling for Transmission Dynamics of Dengue Fever”. Technical Journal, University of Engineering and Technology (UET) Taxila, Pakistan.Vol.21, NO.1, p.116-120. (2016)
5. Bist, S.Riaz, M.Rafiq, Q.A.Chaudhry, S.Farid, “Non-Standard Finite Difference Scheme for The Kinetics’ of Pentaerythritol Production Reactions”. Technical Journal, University of Engineering and Technology (UET) Taxila, Pakistan.Vol.21, NO.1, p.111-115.(2016)
6. A, M. Saeed, N. A. Chaudhry, M. F. Tabassum, M. Rafiq, “Optimal Design of 16 Bar Truss Structure by pattern Search Methods”. Pakistan Journal of Science. Vol. 68 No. 1, p.74-81. (2016)
7. Rafiq, M.O. Ahmad, “Numerical Modeling of Dengue Disease with Incubation Period of Virus”. Pak.J.Engg. &Appl.Sci.Vol. 17, p.19-29.(2015)
8. Riaz, M.Rafiq, Ozair.M.A, “Non-Standard Finite Difference Method for Quadratic Riccati Differential Equation”. PUJM.Vol.47(2), p.49-55. (2015).
9. Basit, S. Riaz, M. Rafiq, Q. A. Chaudhry, S Farid. “Comparison of Numerical Solutions of Pentaerythritol Production Reactions”. Sci. Int. 27(4), p.2965-2968.(2015)
10. Zain Ul Abadin Zafar, Anjum Pervaiz, M. O. Ahmad, Rafiq, “Finite Element Model for Linear Second Order One Dimensional Inhomogeneous Wave Equation”. Pak.J.Engg. &Appl.Sci.Vol. 17, p.58-63. (2015)
11. Sumera K, M. Rafiq, M.O.Ahmed, M.Usman , M.I. Bhatti, “Solution of a  Vaccination  Based SIR Epidemic Model by Homotopy Analysis Method”. Pak.J.Engg. &Appl.Sci.Vol. 15, p.58-67. (2014)
1. Usman, M.O.Ahmed, M.Rafiq, Sumera.K , Mumtaz.A, “Finite Difference Schemes for the determination of Thermal Coefficient and Analysis of its Variation with Time”. Pak.J.Engg. &Appl.Sci.Vol. 15, p.50-57..(2014)
2. Zafar, M. O. Ahmad , A Pervaiz, M. Rafiq. “Fourth Order Compact Method for One Dimensional Inhomogeneous Telegraph Equation with”. Pak.J.Engg. &Appl.Sci.Vol. 14, p.96-101..(2014)
3. Zafar, M.T.Hussain, A.Pervaiz, M. O. Ahmad , M. Rafiq , M.Kalim,“ Finite Element Model for Linear Second Order One Dimensional Homogeneous Telegraph Equation”. Pakistan Journal of Science .Vol. 65 No. 1, p.69-72. (2013)
4. Shabbir, M. Rafiq , M.O.Ahmed, A. Pervaiz ,R. Siddique, “Finite Element Solution For Two Dimensional Laplace Equation With Dirichlet Boundary Conditions”. Pak.J.Engg. &Appl.Sci.Vol. 10, p.97-102. (2012)
5. Rafiq , M.O.Ahmed , S. Ahmed, R. Siddique, A. Pervaiz. “Some Finite Difference Methods for One Dimensional Burgers’ Equation for Irrotational Incompressible Flow Problem”. Pak.J.Engg. &Appl.Sci.Vol. 9, p.13-16. (2011)
6. M.Rafiq, M.O.Ahmad,S,Iqbal. “Finite Element Solution For One Dimensional General Linear Second Order Boundary Value Problem”. Pakistan Journal of Science .Vol. 60 No 3-4, p.21-26. (2008)

#### Submitted Papers

1. Rafiq, M.O. Ahmad, Noor. A. “Numerical Modeling of Transmission Dynamics of Dengue Disease Including Extrinsic Incubation Period (EIP). (IJB-D-15-00084)
2. Rafiq, H. R.Ali , M.O.Ahmed, Nazir.Ahmad , A.Pervaiz. “A Quadratic Finite Element Model For Special Linear Second Order Boundary Value Problems”. (PJEAS-142)
3. Rafiq, Faiza.B, M.O.Ahmed, Nousheen.A, “Finite Element Model For Linear Second Order One Dimensional Wave Equation”. (PJEAS-204)
4. Rafiq, Nousheen.A, M.O.Ahmed, Faiza.B, Zain Ul Abadin Zafar. “Finite Element Model For Linear Second Order One Dimensional Diffusion Equation”. (PJEAS-210)
5. Zain Ul Abadin Zafar, Anjum Pervaiz, M. O. Ahmad, M. Rafiq. “Fourth Order Compact Method for One Dimensional Homogeneous Wave Equation with”. (PJEAS-222)

#### Accepted Papers

1. Zain Ul Abadin Zafar, Kashif Rehan, Muhammad Mushtaq, Muhammad Rafiq. “Numerical Modeling for Nonlinear Biochemical Reaction Networks”. Iranian Journal of Mathematical Chemistry (2016).

#### Conference Proceedings

1. Rafiq, M.O.Ahmad, S.Iqbal, “Numerical Modeling of Internal Transmission Dynamics of Dengue Virus”. Proceedings of 13thInternational Bhurban Conference on Applied Sciences and Technology 2016 (IBCAST-2016) Jan 12-16, 2016.IEEE-Xplore Digital Library, Conference Proceedings , p.85-91. (IBCAST-2016).
2. Rafiq, A.Raza, Rafia, “Numerical Modeling of Transmission Dynamics of Vector-Born Plant Pathogen”. Proceedings of 14thInternational Bhurban Conference on Applied Sciences and Technology 2017 (IBCAST-2017) Jan 10-14, 2017.IEEE-Xplore Digital Library, Conference Proceedings , p.214-219. (IBCAST-2017).
3. Rafiq, A.Raza, A.Anayat, “Numerical Modeling of Virus Transmission in a Computer Network”. Proceedings of 14thInternational Bhurban Conference on Applied Sciences and Technology 2017 (IBCAST-2017) Jan 10-14, 2017.IEEE-Xplore Digital Library, Conference Proceedings , p.414-419. (IBCAST-2017).

#### Conference Talks

1. Numerical Modeling of Transmission Dynamics of HIV/AIDS and Hepatitis C Virus Co-infection
12th Conference on Recent Advances in Mathematical Methods, Models &Applications(RAMMMA), April 8-9, 2017 at Lahore School of Economics (LSE), Lahore
1. Numerical Analysis of an SEIR Epidemic Model with the Effect of Time Delay
12th Conference on Recent Advances in Mathematical Methods, Models &Applications(RAMMMA), April 8-9, 2017 at Lahore School of Economics (LSE), Lahore
1. “Numerical Modeling of Impact of Immunization and Scrapping on Regulating Foot and Mouth Disease”
3rd UMT International Conference on Pure and Applied Mathematics (UICPAM-2017) March 4-6, 2017. Flatties Hotel, Lahore.
1. “Numerical Analysis of a Delayed SIR Epidemic Model with constant Vaccination Strategy”
3rd UMT International Conference on Pure and Applied Mathematics (UICPAM-2017) March 4-6, 2017. Flatties Hotel, Lahore.
1. “Numerical Modeling of Virus Transmission in a Computer Network”
14th International Bhurban Conference on Applied Sciences and Technology 2017 (IBCAST-2017) Jan 10-14, 2017.National Center for Physics (NCP), Islamabad.
1. “Numerical Modeling of Transmission Dynamics of a Vector-Born Plant Pathogen”
14th International Bhurban Conference on Applied Sciences and Technology 2017 (IBCAST-2017) Jan 10-14, 2017.National Center for Physics (NCP), Islamabad.
1. “Numerical Analysis of a Delayed SIR Epidemic Model”
17th International Pure Mathematics Conference-2016 (IPMC-2016) held at Islamabad on Aug 5-7, 2016.
1. “Numerical Modeling of Transmission Dynamics of Computer Virus”
17th International Pure Mathematics Conference-2016 (IPMC-2016) held at Islamabad on Aug 5-7, 2016.
1. “Non-Standard Finite Difference Predictor-Corrector Method for Quadratic Riccati Differential Equation”
CASM International Conference on Differential Equations and Applications, May 26-28,2016 at Lahore University of Management Sciences(LUMS), Lahore
1. “Numerical Modeling for Transmission Dynamics of Dengue Disease in Pregnant and Non-Pregnant Patients”
11th Conference on Recent Advances in Mathematical Methods, Models &Applications(RAMMMA), April 9-10, 2016 at Lahore School of Economics (LSE), Lahore.
1. “Numerical Modeling of Transmission Dynamics of Ebola Virus”
1st UMT International Conference on Pure and Applied Sciences (UICPAS-2016) March 5-7, 2016. University of Management Sciences (UMT), Lahore.
1. “Non-Standard Finite Difference Solution for a Chemical Kinetics System”
1st UMT International Conference on Pure and Applied Sciences (UICPAS-2016) March 5-7, 2016. University of Management Sciences (UMT), Lahore.
1. “Numerical Modeling of Internal Transmission Dynamics of Dengue Virus”
13th International Bhurban Conference on Applied Sciences and Technology 2016 (IBCAST-2016) Jan 12-16, 2016.National Center for Physics (NCP), Islamabad.
1. “A Predictor Correct Non-Standard Finite Difference Scheme for SEIR Epidemic Model”
International Conference on Recent Advances in Applied Mathematics (ICRAAM) held at COMSATS Institute of Information Technology, Lahore on Dec 17-18, 2015.
1. “Numerical Modeling for HIV Infection of CD4+ T Cells”
3rd International Conference on Emerging trends in Bioinformatics and Biosciences (ICETBB-2015) held at Mohammad Ali Jinnah University, Islamabad on October 3rd, 2015.
1. “Numerical Modeling of Transmission Dynamics of Chickenpox (varicella zoster virus)”
16th International Pure Mathematics Conference-2015 (IPMC-2015) held at Islamabad on Aug 21-23, 2015.
1. “Numerical Modeling of Transmission Dynamics of Bird-Flu”
10th Conference on Recent Advances in Mathematical Methods, Models &Applications(RAMMMA), April 11-12, 2015 at Lahore School of Economics (LSE), Lahore.
1. “Numerical Modeling of Transmission Dynamics of Influenza with Constant Vaccination Strategy”
Two Days International Conference on Pure and Applied Mathematics (ICPAM-2015) March 9-10, 2015. University of Sargodha (UOS), Sargodha.
1. “Numerical Modeling of Transmission Dynamics of HIV/AIDS”
1st UMT National Conference on Pure and Applied Mathematics (UNCPAM-2015) March 7-8, 2015. University of Management Sciences (UMT), Lahore.
1. “Numerical Modeling of Transmission Dynamics of Dengue Disease including Extrinsic Incubation Period”
12th International Bhurban Conference on Applied Sciences and Technology 2015 (IBCAST-2015) Jan 13-17, 2015.National Center for Physics (NCP), Islamabad.
1. “Numerical Modeling of Dengue Disease with Incubation Period of Virus”
9th Conference on Recent Advances in Mathematical Methods, Models &Applications(RAMMMA), April 19-20, 2014 at Lahore School of Economics (LSE), Lahore.
1. “Numerical Modeling of Transmission Dynamics of Dengue Fever”
14th International Pure Mathematics Conference-2013 (IPMC-2013) held at Islamabad on Aug 23-25, 2013.
1. “Numerical Approach to a SIR epidemic model with constant vaccination strategy”
8th Conference on Recent Advances in Mathematical Methods, Models &Applications, April 13-14, 2013 at HEC regional office Lahore.
1. “Finite Element Method for Special Linear Second Order Boundary Value Problems” Winter conference in Mathematics (December30-31,2010) held at Center for Advanced Studies in Mathematics(CASM), Lahore University of Management Sciences (LUMS) Lahore.
2. “Finite Element Solution for Two Dimensional Laplace Equation with Dirichlet Boundary Conditions”
Summer Conference in Mathematics, July 27-28, 2009 at Lahore University of Management Sciences Lahore, Pakistan.
3. “Applications of Matrices in Cryptography”
UCP-IEEEP’09, Multi-Topic Conference, May 27, 2009 at University of Central Punjab Lahore.

#### Contact

(042) 35880007 (151)
m.rafiq@ucp.edu.pk
University of Central Punjab Faculty of Electrical Engineering