A lot of focus in theoretical ecology has been on equilibria and absorbing sets, but there is growing interest in non-asymptotic behaviours that last for a very long time. Models of fishing systems may feature "population collapses" wherein biomass can temporarily crash to very low levels despite strict management efforts. Epidemiological models can produce a prolonged period of low disease incidence called a "honeymoon period" after the onset of mass vaccination efforts that ends with a resurgence. These transient phenomena have been observed in data persisting for decades. Our aim is to expand our theoretical framework on long transient dynamics with a focus on those arising in ecological systems. This work involves techniques in nonlinear analysis of various types of differential equation systems.

*Some representative publications*

A. Liu*, F.M.G. Magpantay and K. Abdella (2023)

A framework for long-lasting, slowly varying transient dynamics

*Math. Biosci. Eng.*20(7): 12130-12153A. Liu* and F.M.G. Magpantay (2022)

A quantification of long transient dynamics

*SIAM J. Appl. Math.*82(2): 381-407N. Akhavan Kharazian* and F.M.G. Magpantay (2020)

The honeymoon period after mass vaccination

*Math. Biosci. Eng.*18(1): 354–372F.M.G. Magpantay, A.A. King and P. Rohani (2019)

Age-structure and transient dynamics in epidemiological systems

*J. Royal Soc. Interface*16(156): 20190151

Infectious diseases are among the top ten causes of death around the world, and are the leading causes of death for children in low-income countries. Mathematical modeling is a powerful tool for studying many types of complex systems, including the spread of infectious diseases. We combine modern techniques from analysis and applied mathematics with innovative methods in scientific computing to tackle high-dimensional and multi-faceted modeling problems.

*Some representative publications*

A. Le*, A.A. King, F.M.G. Magpantay, A. Mesbahi and P. Rohani (2021)

The impact of different types of infection-derived immunity

*J. Math. Biol.*83(6-7):61L. Xue*, X. Ren, F.M.G. Magpantay, W. Sun and H. Zhu (2021)

Optimal control of mitigation strategies for dengue virus transmission.

*Bull. Math. Bio.*83(8)N. Akhavan Kharazian and F.M.G. Magpantay (2020)

The honeymoon period after mass vaccination

*Math. Biosci. Eng.*18(1): 354–372F.M.G. Magpantay, A.A. King and P. Rohani (2019)

Age-structure and transient dynamics in epidemiological systems

*J. Royal Soc. Interface*16(156): 20190151M. Domenech de Celles, F.M.G. Magpantay, A.A. King and P. Rohani (2018)

The impact of past vaccination coverage and immunity on pertussis resurgence

*Sci. Transl. Med.*10(434)F.M.G. Magpantay (2017)

Vaccine impact in homogeneous and age-structured models

*J. Math. Biol.*75(6–7): 1591–1617

Delay differential equations (DDEs) are differential equations wherein the rate of change of the state of the system depends on values at previous times. Much of the theory on DDEs focus on constant and time-dependent delays, but many delays are naturally state-dependent (SD). In disease systems for instance, we can expect that the response time to implement disease controls would be more urgent in the face of larger outbreaks. Ignoring state-dependence in a model can lead to incorrect conclusions since state-dependence can induce dynamics that would be absent in corresponding constant delay systems. We work on both the theory and applications of SD-DDEs, especially with regards to biomathematics.

*Some representative publications*

A.R. Humphries and F.M.G. Magpantay (2021)

Lyapunov-Razumikhin techniques for state-dependent delay differential equations

*J. Differential Equations*304: 287-325F.M.G. Magpantay and A.R. Humphries (2020)

Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations

*Discrete Continuous Dyn. Sys. Ser. S*13: 85–104J.A. Collera and F.M.G. Magpantay (2018)

Dynamics of a stage-structured intraguild predation model

*Proceedings of the AMMCS 2017*F.M.G. Magpantay and N. Kosovalic (2015)

An age-structured population model with state-dependent delay: Dynamics

*12th IFAC Workshop on Time Delay Systems*

* Asterisks denote students or postdoctoral fellows from my research group.