Coronavirus disease 2019 (COVID-19) is a disease caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as pandemic disease. The disease has neither approved medicine nor vaccine and has made governments and scholars search for drastic measures in combating the pandemic. Regrettably, the spread of the virus and mortality due to COVID-19 has continued to increase daily. Hence, it is imperative to control the spread of the disease particularly using nonpharmacological strategies such as quarantine, isolation, and public health education. This work studied the effect of these different control strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contributions in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number and effective reproduction numbers were computed with and without interventions, respectively, and were used to carry out the sensitivity analysis that identified the critical parameters contributing to the spread of COVID-19. The optimal control analysis was carried out using the Pontryagin’s maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings of the optimal control analysis and numerical simulations revealed that time-dependent interventions reduced the number of exposed and infected individuals compared to time-independent interventions. These interventions were time-bound and best implemented within the first 100 days of the outbreak. Again, the combined implementation of only two of these interventions produced a good result in reducing infection in the population. While, the combined implementation of all three interventions performed better, even though zero infection was not achieved in the population. This implied that multiple interventions need to be deployed early in order to reduce the virus to the barest minimum.

This study presents a deterministic model for the environmental transmission dynamics of monkeypox (MPX) in the presence of quarantine and vaccination. The analysis of the model established three important equilibrium states namely; monkeypox-free equilibrium (MPXV-FE), infected rodent-free endemic equilibrium (IRF-EE), and coexistence equilibrium (CO-EE). The local and global stability of the equilibrium states is examined in terms of reproduction numbers. For global stability, the comparison theory is used for MPXV-FE while the Voltera-Lyapunov matrix theory is used for IRF-EE. Sensitivity analysis is performed using the Latin hypercube sampling method, and the results showed that environmental transmission parameters are the main driver of infection in the dynamics of MPX infection. This is further supported by numerical simulations to show the impact of environmental transmission on the MPX infection and also the validity of the theoretical analysis. Based on the results, it is recommended that health practitioners and policy-makers should constitute control strategies that will focus on reducing transmission and shedding of the virus in the environment while increasing the environmental decay rate of the MPXV. This will complement the quarantine and vaccination strategies in place.

Coronavirus disease 2019 (COVID-19) is a disease caused by Severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as pandemic disease. The disease has neither approved medicine nor vaccine and has made government and scholars search for drastic measures in combating the pandemic. Regrettably, the spread of the virus and mortality due to COVID-19 has continued to increase daily. Hence, it is imperative to control the spread of the disease particularly using non-pharmacological strategies such as quarantine, isolation and public health education. This work studied the effect of these different control strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contributions in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number was computed with and without interventions and was used to carry out the sensitivity analysis that identified the critical parameters contributing to the spread of COVID-19. The optimal control analysis was carried out using the Pontryagin’s maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings of the optimal control analysis and numerical simulations revealed that time-dependent interventions reduced the number of exposed and infected individuals compared to time-independent interventions. These interventions were time-bound and best implemented within the first 100 days of the outbreak. Again, the combined implementation of only two of these interventions produced a good result in reducing infection in the population, while the combined implementation of all three interventions performed better, even though zero infection was not achieved in the population. This implied that multiple interventions need to be deployed early in order to the virus to the barest minimum.

Schistosomiasis is a neglected disease affecting almost every region of the world, with its endemicity mainly experience in sub-Saharan Africa. It remains difficult to eradicate due to heterogeneity associated with its transmission mode. A mathematical model of Schistosomiasis integrating heterogeneous host transmission pathways is thus formulated and analyzed to investigate the impact of the disease in the human population. Mathematical analyses are presented, including establishing the existence and uniqueness of solutions, computation of the model equilibria, and the basic reproduction number (R₀). Stability analyses of the model equilibrium states show that disease-free and endemic equilibrium points are locally and globally asymptotically stable whenever R₀ < 1 and R₀>1, respectively. Additionally, bifurcation analysis is carried out to establish the existence of a forward bifurcation around R₀ = 1. Using Latin-hypercube sampling, global sensitivity analysis was performed to examine and investigate the most significant model parameters in R₀ which drives the infection. The sensitivity analysis result indicates that the snail's natural death rate, cercariae, and miracidia decay rates are the most influential parameters. Furthermore, numerical simulations of the model were done to show time series plots, phase portraits, and 3-D representations of the model and also to visualize the impact of the most sensitive parameters on the disease dynamics. Our numerical findings suggest that reducing the snail population will directly reduce Schistosomiasis transmission within the human population and thus lead to its eradication.

Despite the lifting of COVID-19 restrictions, the COVID-19 pandemic and its effects remain a global challenge including the sub-Saharan Africa (SSA) region. Knowledge of the COVID-19 dynamics and its potential trends amidst variations in COVID-19 vaccine coverage is therefore crucial for policy makers in the SSA region where vaccine uptake is generally lower than in high-income countries. Using a compartmental epidemiological model, this study aims to forecast the potential COVID-19 trends and determine how long a wave could be, taking into consideration the current vaccination rates. The model is calibrated using South African reported data for the first four waves of COVID-19, and the data for the fifth wave are used to test the validity of the model forecast. The model is qualitatively analysed by determining equilibria and their stability, calculating the basic reproduction number R 0 and investigating the local and global sensitivity analysis with respect to R 0 . The impact of vaccination and control interventions are investigated via a series of numerical simulations. Based on the fitted data and simulations, we observed that massive vaccination would only be beneficial (deaths averting) if a highly effective vaccine is used, particularly in combination with non-pharmaceutical interventions. Furthermore, our forecasts demonstrate that increased vaccination coverage in SSA increases population immunity leading to low daily infection numbers in potential future waves. Our findings could be helpful in guiding policy makers and governments in designing vaccination strategies and the implementation of other COVID-19 mitigation strategies.