Nature computing has evolved with exciting performance to solve complex real-world combinatorial optimization problems. These problems span across engineering, medical sciences, and sciences generally. The Ebola virus has a propagation strategy that allows individuals in a population to move among susceptible, infected, quarantined, hospitalized, recovered, and dead sub-population groups. Motivated by the effectiveness of this strategy of propagation of the disease, a new bio-inspired and population-based optimization algorithm is proposed. This study presents a novel metaheuristic algorithm named Ebola optimization search algorithm (EOSA) based on the propagation mechanism of the Ebola virus disease. First, we designed an improved SIR model of the disease, namely SEIR-HVQD: Susceptible (S), exposed (E), Infected (I), Hospitalized (H), recovered (R), Vaccinated (V), Quarantine (Q), and Death or death (D). Secondly, we represented the new model using a mathematical model based on a system of first-order differential equations. A combination of the propagation and mathematical models was adapted for developing the new metaheuristic algorithm. To evaluate the performance and capability of the proposed method in comparison with other optimization methods, two sets of benchmark functions consisting of forty-seven (47) classical and thirty (30) constrained IEEE-CEC benchmark functions were investigated. The results indicate that the performance of the proposed algorithm is competitive with other state-of-the-art optimization methods based on scalability, convergence, and sensitivity analyses. Extensive simulation results show that the EOSA outperforms popular metaheuristic algorithms such as the Particle Swarm Optimization Algorithm (PSO), Genetic Algorithm (GA), and Artificial Bee Colony Algorithm (ABC). Also, the algorithm was applied to address the complex problem of selecting the best combination of convolutional neural network (CNN) hyperparameters in the image classification of digital mammography. Results obtained showed the optimized CNN architecture successfully detected breast cancer from digital images at an accuracy of 96.0.