arXiv subjects

F. M. G. Magpantay

Publications and source records attributed to F. M. G. Magpantay.

4 recordsLinked to original sources

arXiv2024

Edge-based Modeling for Disease Transmission on Random Graphs: An Application to Mitigate a Syphilis Outbreak

Edge-based network models, especially those based on bond percolation methods, can be used to model disease transmission on complex networks and accommodate social heterogeneity while keeping tractability. Here we present an application of an edge-based network model to the spread of syphilis in the Kingston, Frontenac and Lennox & Addington (KFL&A) region of Southeastern Ontario, Canada. We compared the results of using a network-based susceptible-infectious-recovered (SIR) model to those generated from using a traditional mass action SIR model. We found that the network model yields very different predictions, including a much lower estimate of the final epidemic size. We also used the network model to estimate the potential impact of introducing a rapid syphilis point of care test (POCT) and treatment intervention strategy that has recently been implemented by the public health unit to mitigate syphilis transmission.

q-bio.PE↗

arXiv2024

Disease Transmission on Random Graphs Using Edge-Based Percolation

Edge-based percolation methods can be used to analyze disease transmission on complex social networks. This allows us to include complex social heterogeneity in our models while maintaining tractability. Here we review the seminal works on this field by Newman et al (2001); Newman (2002, 2003), and Miller et al (2012). We present a systematic discussion of the theoretical background behind these models, including an extensive derivation of the major results. We also connect these results relate back to the classical literature in random graph theory Molloy and Reed (1995, 1998). Finally, we also present an accompanying R package that takes epidemic and network parameters as input and generates estimates of the epidemic trajectory and final size. This manuscript and the R package was developed to help researchers easily understand and use network models to investigate the interaction between different community structures and disease transmission.

cs.SI↗

arXiv2020

Lyapunov-Razumikhin techniques for state-dependent delay differential equations

We present Lyapunov stability and asymptotic stability theorems for steady state solutions of general state-dependent delay differential equations (DDEs) using Lyapunov-Razumikhin methods. Our results apply to DDEs with multiple discrete state-dependent delays, which may be nonautonomous for the Lyapunov stability result, but autonomous (or periodically forced) for the asymptotic stability result. Our main technique is to replace the DDE by a nonautonomous ordinary differential equation (ODE) where the delayed terms become source terms in the ODE. The asymptotic stability result and its proof are entirely new, and based on a contradiction argument together with the Arzela-Ascoli theorem. This approach alleviates the need to construct auxiliary functions to ensure the asymptotic contraction, which is a feature of all other Lyapunov-Razumikhin asymptotic stability results of which we are aware. We apply our results to a state-dependent model equation which includes Hayes equation as a special case, to directly establish asymptotic stability in parts of the stability domain along with lower bounds on the size of the basin of attraction.

math.DS↗

arXiv2017

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

We present generalised Lyapunov-Razumikhin techniques for establishing global asymptotic stability of steady-state solutions of scalar delay differential equations. When global asymptotic stability cannot be established, the technique can be used to derive bounds on the persistent dynamics. The method is applicable to constant and variable delay problems, and we illustrate the method by applying it to the state-dependent delay differential equation known as the sawtooth equation, to find parameter regions for which the steady-state solution is globally asymptotically stable. We also establish bounds on the periodic orbits that arise when the steady-state is unstable. This technique can be readily extended to apply to other scalar delay differential equations with negative feedback.

math.DS↗