SARS COV-2 (Covid-19) has imposed a monumental socio-economic burden worldwide, and its impact still lingers. We propose a deterministic model to describe the transmission dynamics of Covid-19, emphasizing the effects of vaccination on the prevailing epidemic. The proposed model incorporates current information on Covid-19, such as reinfection, waning of immunity derived from the vaccine, and infectiousness of the pre-symptomatic individuals into the disease dynamics. Moreover, the model analysis reveals that it exhibits the phenomenon of backward bifurcation, thus suggesting that driving the model reproduction number below unity may not suffice to drive the epidemic toward extinction. The model is fitted to real-life data to estimate values for some of the unknown parameters. In addition, the model epidemic threshold and equilibria are determined while the criteria for the stability of each equilibrium solution are established using the Metzler approach. A sensitivity analysis of the model is performed based on the Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCCs) approaches to illustrate the impact of the various model parameters and explore the dependency of control reproduction number on its constituents parameters, which invariably gives insight on what needs to be done to contain the pandemic effectively. The foregoing notwithstanding, the contour plots of the control reproduction number concerning some of the salient parameters indicate that increasing vaccination coverage and decreasing vaccine waning rate would remarkably reduce the value of the reproduction number below unity, thus facilitating the possible elimination of the disease from the population. Finally, the model is solved numerically and simulated for different scenarios of disease outbreaks with the findings discussed.

This study explores Mpox transmission dynamics using a mathematical and data-driven epidemiological model that incorporates two viral strains, Clade I and Clade II. The model includes transmission pathways between humans and mammals and divides the human population into susceptible, exposed, infectious, hospitalized, and recovered groups. Weekly data from the WHO for Spain, Italy, Nigeria, and the DRC from 2022 to 2024 are used for model validation via non-linear least-squares fitting, with model performance assessed by Root Mean Squared Error (RMSE). We conduct time-series analysis to detect trends and anomalies in Mpox cases, with scenario simulations examining strain-specific transmission and the basic reproduction number (${\mathcal{R}}_0)$. The mathematical model fit is compared with two statistical model fits to emphasize the importance of developing a model that incorporates Mpox strain. Mathematical analysis confirms the model’s key properties, including positivity, boundedness, and equilibrium stability. Results underscore the importance of strain-specific dynamics and varying infection proportions for ${\mathcal{R}}_0$. This study combines mathematical rigor with empirical data to provide valuable insights into Mpox transmission and offers a framework for understanding multi-strain pathogens in diverse populations. Results from the simulation indicate that an increase in the effective contact rate leads to the dominance of the prevalent Mpox Clades in each country. Based on these findings, we recommend the implementation of strategies aimed at reducing the effective contact rate to control the spread of the virus strains.

This study investigates optimal intervention strategies for controlling the spread of two co-circulating strains of SARS-CoV-2 within the Nigerian population. A newly formulated epidemiological model captures the transmission dynamics of the dual-strain system and incorporates three key control mechanisms: vaccination, non-pharmaceutical interventions (NPIs), and therapeutic treatment. To identify the most effective approach, Pontryagin’s Maximum Principle is employed, enabling the derivation of an optimal control function that minimizes both infection rates and associated implementation costs. Through numerical simulations, this study evaluates the performance of individual, paired, and combined intervention strategies. Additionally, a cost-effectiveness assessment based on the Incremental Cost-Effectiveness Ratio (ICER) framework highlights the most economically viable option, while results suggest that the combined application of vaccination and treatment strategies offers superior control over dual-strain transmission and implementing all three strategies together ensures the most robust suppression of the outbreak.

The emergence of a coronavirus disease (COVID-19) pandemic caused by severe acute respiratorysyndrome coronavirus 2 (SARS-COV 2) has caused an unprecedented global societal andpublic health crisis. A novel variable (genetically resistant humans, which they serve as reservoirhost) that could influence the prevalence of COVID-19 pandemic have been incorporatedand analyzed rigorously. Detection and testing for COVID-19 (in humans that are geneticallyresistant to COVID-19), proper preventive measures, and timely medical care are essential inmanaging and controlling COVID-19 outbreak. First, we analyze the disease-free state of theCOVID-19 model, calculate the baseline control reproduction number, and obtain the localstability of disease-free equilibrium. The model is calibrated using data obtained from NigeriaCentre for Disease Control and key parameters of the model are estimated. Sensitivity analysisis carried out to investigate the influence of the parameters in curtailing the disease. Numericalsimulations are then used to explore the behaviour of the model solutions involving the novelvariable (genetically resistant humans) and control measures. Our results suggest that strictintervention effort (early detection of genetically resistant individuals, testing and isolation ofthe infected individuals) is required for quick suppression of the disease.