Mathematical Modeling and Stability Analysis of Monkey Pox Transmission in Rodents and Humans

Abstract

In this thesis, deterministic and stochastic mathematical models for the dynamics of monkey pox transmission across rodent and human populations are developed and analyzed. The study builds systems of nonlinear differential equations to describe disease progression and control strategies, such as vaccination and treatment, using compartmental modeling techniques like SIR and SEIR. Important epidemiological characteristics like interspecies transmission, disease-induced mortality, and incubation times are included in the models. To evaluate the stability of endemic and disease-free equilibria, analytical techniques such as basic reproduction number (R₀) analysis and Jacobian matrices are used. Moreover, random environmental and demographic perturbations are taken into account via stochastic differential equations, and stochastic Euler, Runge-Kutta, and NSFD methods are employed for numerical simulations. The results demonstrate the importance of intervention tactics in lowering the incidence of monkey pox and the usefulness of stochastic modeling in comprehending intricate epidemic dynamics in the face of uncertainty.