Next‐Generation Matrix Approach for Computing the Basic Reproduction Number of Infectious Diseases

Abstract

ABSTRACT Understanding how diseases spread is crucial for effective public health planning, and the basic reproduction number ( ) plays a key role in this process. This study considers the application of a next‐generation matrix (NGM) to compute the basic reproduction number of different compartmental models: SIR, SEIR, SEITR, , and , depicting the initial state of the diphtheria outbreak and intervention strategies. The aim is to develop various domains of the NGM using different modeling approaches, providing strategic guidance on how vaccines and treatments can be optimally used to control and potentially eliminate diphtheria in Nigeria. The transmission equations for basic reproduction numbers were derived from each compartmental model considered. Using simulated data at three transmission levels (0.1, 0.5, and 1.0), we found average values of 0.1310, 0.0378, 0.0284, 0.0378, and 0.0284 for the respective models. We also analyzed real‐world data on diphtheria cases reported by the Nigeria Centre for Disease Control between February 2003 and December 2023. From this, we obtained similar trends, with average values of 0.5251, 0.4069, 0.0002899, 0.4069, and 0.0002899 across the different model structures. As models became more complex, accounting for stages like exposure, treatment, and vaccination, values tended to decrease. Interestingly, we found that whether we used large, classical, or small domains within the NGM framework, the computed remained the same across each model structure. This consistency highlights the strength and flexibility of the NGM approach in understanding and comparing the spread potential of infectious diseases.