Compartmental model for the spread of infectious disease with hererogenous population: a case study of COVID-19 and Lassa fever

Abstract

This study investigates the transmission dynamics of COVID-19 and Lassa fever, with particular attention to the risks and implications of co-infection. By dividing the human population into epidemiological compartments, the models capture the real course of disease spread in a structured and realistic way. The mathematical correctness of the models was validated by proving positivity, boundedness, and reliability of solutions for public health interpretation. For COVID-19, the basic SYR framework was analysed to obtain the reproduction number RY , and the model was further extended to an SEAIHR structure to include exposed, asymptomatic, infectious, and hospitalised individuals. For Lassa fever, a deterministic compartmental model was developed and subjected to stability analysis. Numerical simulations were carried out for both diseases to assess intervention strategies and transmission behaviour. The COVID–19 analysis revealed that the disease can be eliminated when RY < 1, but once RY > 1, infection becomes persistent. The extended SEAIHR model also produced the overall reproduction number R0, showing how reductions in contact rates, timely detection, effective hospital care, and faster recovery can substantially suppress transmission. For Lassa fever, the disease-free equilibrium remained stable only when the reproduction number was kept below one. Simulations highlighted the significant influence of asymptomatic carriers and showed that no single intervention— whether treatment, health education, or rodent control—can fully control the disease on its own. Instead, the most meaningful reduction in cases occurred when human-focused measures were combined with strong rodent control, leading to the elimination of infectious rodents by the 35th day. Together, these results emphasise the urgency of studying co-infections in regions such as West Africa, where both diseases circulate at the same time. Incorporating optimal control theory provides a systematic and cost-effective framework for coordinating interventions across multiple pathways of transmission. This study therefore deepens our understanding of the dynamics of both COVID– 19 and Lassa fever and offers practical insights for improving interventions, epivdemic preparedness, and public health responses. The centre-manifold analysis further shows that both models experience a forward transcritical bifurcation at R0 = 1: once transmission exceeds this threshold, a stable endemic state emerges. This reinforces a critical message—maintaining transmission below the threshold is essential for preventing long-term persistence of either disease.