Sub-Saharan Africa harbours the majority of the burden of Lassa fever. Clinical diseases, as well as high seroprevalence, have been documented in Nigeria, Sierra Leone, Liberia, Guinea, Ivory Coast, Ghana, Senegal, Upper Volta, Gambia, and Mali. Deaths from Lassa fever occur all year round but naturally peak during the dry season. Annually, the number of people infected is estimated at 100,000 to 300,000, with approximately 5,000 deaths. There have been some work done on the dynamics of Lassa fever disease transmission, but to the best of our knowledge, none has been able to capture the seasonal variation of Mastomys rodent population and its impact on the transmission dynamics. In this work, a periodically forced seasonal nonautonomous system of a nonlinear ordinary differential equation is developed that captures the dynamics of Lassa fever transmission and seasonal variation in the birth of Mastomys rodents where time was measured in days to capture seasonality. It was shown that the model is epidemiologically meaningful and mathematically well posed by using the results from the qualitative properties of the solution of the model. A time-dependent basic reproduction number RLt is obtained such that its yearly average is written as R˜L<1, when the disease does not invade the population (means that the number of infected humans always decreases in the seasons of transmission), and R˜L>1, when the disease remains constantly and is invading the population, and it was detected that R˜L≠RL. We also performed some evaluation of the Lassa fever disease intervention strategies using the elasticity of the equilibrial prevalence in order to predict the optimal intervention strategies that can be useful in guiding the local national control program on Lassa fever disease to make a proper decision on the intervention packages. Numerical simulations were carried out to illustrate the analytical results, and we found that the numerical simulations of the model showed that possible combined intervention strategies would reduce the spread of the disease. It was established that, to eliminate Lassa fever disease, treatments with ribavirin must be provided early to reduce mortality and other preventive measures like an educational campaign, community hygiene, isolation of infected humans, and culling/destruction of rodents must be applied to also reduce the morbidity of the disease. Finally, the obtained results gave a primary framework for planning and designing cost-effective strategies for good interventions in eliminating Lassa fever.

Many mathematical models have explored the dynamics of cholera but none have been used to predict the optimal strategies of the three control interventions (the use of hygiene promotion and social mobilization; the use of treatment by drug/oral re-hydration solution; and the use of safe water, hygiene, and sanitation). The goal here is to develop (deterministic and stochastic) mathematical models of cholera transmission and control dynamics, with the aim of investigating the effect of the three control interventions against cholera transmission in order to find optimal control strategies. The reproduction number $R_p$ was obtained through the next generation matrix method and sensitivity and elasticity analysis were performed. The global stability of the equilibrium was obtained using the Lyapunov functional. Optimal control theory was applied to investigate the optimal control strategies for controlling the spread of cholera using the combination of control interventions. The Pontryagin’s maximum principle was used to characterize the optimal levels of combined control interventions. The models were validated using numerical experiments and sensitivity analysis was done. Optimal control theory showed that the combinations of the control intervention influenced disease progression. The characterisation of the optimal levels of the multiple control interventions showed the means for minimizing cholera transmission, mortality, and morbidity in finite time. The numerical experiments showed that there are fluctuations and noise due to its dependence on the corresponding population size and that the optimal control strategies to effectively control cholera transmission, mortality, and morbidity was through the combinations of all three control interventions. The developed models achieved the reduction, control, and/or elimination of cholera through incorporating multiple control interventions.

The World Health Organization (WHO) declared mpox a Public Health Emergency of International Concern (PHEIC) twice, in response to the global outbreak, first in May 2022 and again in August 2024, after a span of 2 years and 3 months. African countries continue to be a hotspot for the ongoing mpox outbreaks and Nigeria has contributed substantially in exporting the virus to other countries, highlighting the need for an in-depth analysis of outbreak patterns and forecasting to inform public health policy. This study used the Auto-Regressive Integrated Moving Average (ARIMA) model to perform a 14-month forecast of mpox cases and mortality in Nigeria using mpox monthly routine data. The data were split into two portions; 70% for training, used to estimate the parameters of the forecasting model and 30% for testing, used to evaluate the model’s accuracy. Wavelet analysis was used to decompose the time series into its various frequency components, enabling a multi-resolution analysis of the data. The ARIMA model forecasted an average of 13 mpox cases per month and zero mortality over a 14-month period. The wavelet power spectrum revealed a strong annual cycle between June 2022 and June 2023. In order to sustain the forecasted downward trend in mpox cases in the coming months, it is essential that the National Mpox Technical Working Group (TWG) of Nigeria Centre for Disease Control and Prevention (NCDC) continue to coordinate scale up of vaccine coverage and improve surveillance especially in high risk area. The findings will ultimately improve focused interventions and knowledge of mpox outbreak patterns by guiding public health policy, allocating resources optimally, and preparing health systems for potential outbreaks.

Let \(\Delta _{p,\phi }\) be the weighted p-Laplacian defined on a smooth metric measure space. We study the evolution and monotonicity formulas for the first eigenvalue, \(\lambda _{1}=\lambda (\Delta _{p,\phi })\), of \(\Delta _{p,\phi }\) under the Ricci-harmonic flow. We derive some monotonic quantities involving the first eigenvalue, and as a consequence, this shows that \(\lambda _{1}\) is monotonically nondecreasing and almost everywhere differentiable along the flow existence.