Modeling Infectious Disease Spread: Differential Equations in Population Dynamics and Epidemiology

Abstract

Quantitative modelling of epidemiological diseases plays a vital role in disease dynamics and monitoring and surveillance. Differential equations provide a good way of understanding disease transmission dynamics, and the effectiveness of different mitigation measures. This paper aims at discussing the application of differential equations in studying diseases spreading, particularly with reference to compartmental models like SIR model, and extensions for their improved realism. The paper focuses on the fundamental aspects of differential equations used in population dynamics, epidemics, immunity and vaccines, and the consequences of controlling or changing different aspects of communities. By applying these two models, the paper gives case details concerning the transmission of diseases such as covid 19 and influenza. The findings offer details of disease spread and extension and will serve as a basis for further studies and eventual treatment on the subject in the health sector.