Research Article Novel Numerical Estimates of the Pneumonia and Meningitis EpidemicModelviatheNonsingularKernelwithOptimalAnalysis Saima Rashid , 1 Bushra Kanwal , 2 Abdulaziz Garba Ahmad , 3 Ebenezer Bonyah , 4 and S.K. Elagan 5,6 1 Department of Mathematics, Government College University, Faisalabad 38000, Pakistan 2 Department of Mathematics, COMSATS University, Islamabad, Pakistan 3 Department of Mathematics, National Mathematical Centre Abuja, Abuja 900211, Nigeria 4 Department of Mathematics Education, University of Education, Winneba, Kumasi Campus, Ghana 5 Department of Mathematics and Computer Sciences, Faculty of Science Menoufia University, Shebin, Elkom 32511, Egypt 6 Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia Correspondence should be addressed to Ebenezer Bonyah; ebonyah@aamusted.edu.gh Received 10 April 2022; Accepted 30 May 2022; Published 31 July 2022 Academic Editor: Fathalla A. Rihan Copyright © 2022 Saima Rashid et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this article, we investigated a deterministic model of pneumonia-meningitis coinfection. Employing the Atangana–Baleanu fractional derivative operator in the Caputo framework, we analyze a seven-component approach based on ordinary differential equations (DEs). Furthermore, the invariant domain, disease-free as well as endemic equilibria, and the validity of the model’s potential results are all investigated. According to controller design evaluation and modelling, the modulation technique devised is effective in diminishing the proportion of incidences in various compartments. A fundamental reproducing value is generated by exploiting the next generation matrix to assess the properties of the equilibrium. e system’s reliability is further evaluated. Sensitivity analysis is used to classify the impact of each component on the spread or prevention of illness. Using simulation studies, the impacts of providing therapy have been determined. Additionally, modelling the appropriate configuration dem- onstrated that lowering the fractional order from 1 necessitates a rapid initiation of the specified control technique at the largest intensity achievable and retaining it for the bulk of the pandemic’s duration. 1.Introduction Fractional calculus has gained popularity over the years for representing a plethora of new challenges in fields such as computational virology, quantum theory, technology, and numerous others, wherein fractional-order (FO) operators are either singular (Caputo derivative and Riemann–Liou- ville (RL) fractional derivatives) or nonsingular (Atanga- na–Baleanu and Caputo–Fabrizio derivatives) [1–4]. However, the variation between integer-order and FO derivatives is that the integer-order derivative depicts the functionality of a complex nonlinear network for the entirety of the period, whereas the FO derivative operator represents a characteristic of a logistic scheme for the enormous moment. Furthermore, the integer-order derivative reflects a dynamic state’s spatial information, while the FO derivative formulation of a complex process encompasses the project process domain [5–8]. On the other hand, in modelling specific cases, implementing derivation operators via non- integer values is critical for articulating generational re- quirements and the reliability of memories as a key component of various systems [9, 10]. erefore, the advent of multiple meanings of a frac- tional derivative is fascinating and creates an incentive to identify the intricacies of natural surroundings in the context that certain challenges in existence pursue the index law for the RL fractional operator, some also implement the Mittag- Leffler (ML) rules for the Atangana–Baleanu fractional Hindawi Complexity Volume 2022, Article ID 4717663, 25 pages https://doi.org/10.1155/2022/4717663