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 delves into the dynamics of lymphatic filariasis and buruli ulcer coinfection, two overlooked yet impactful tropical diseases. With lymphatic filariasis, commonly referred to as elephantiasis, and buruli ulcer, a chronic affliction caused by mycobacterium ulcerans, both posing significant health challenges, understanding their interaction is crucial. Utilizing a mathematical model, this research aims to analyze the dynamics of this coinfection, elucidating its complexities. The study establishes the local asymptotic stability of the disease-free equilibrium and calculates the basic reproduction number using the next generation matrix. It uncovers transcritical and backward bifurcation phenomena within the model. Additionally, the integration of time-dependent controls enables the exploration of optimal disease management strategies. Numerical simulations highlight the efficacy of employing a comprehensive approach, utilizing all available controls simultaneously, as the most effective strategy for disease control. These findings underscore the importance of integrated interventions in combating lymphatic filariasis and buruli ulcer coinfection, offering valuable insights for public health policymakers and practitioners.

In this paper, A 6 (six) compartmental (S, I U , I S , I A , Q, R) model was presented to examine the dynamical behavior of disease transmission in the system with quarantine effect on the symptomatic infected, asymptomatic infected and Reproduction number R 0 within a given population. The parameters model was analyzed and estimated experimentally using the real data of COVID-19 confirmed cases for Ethiopia via MATLAB 2021a. Reproduction number R 0 which is a key indicator to whether a disease outbreak spread force will persist or die out within population. R 0 was found using the next generation matrix with Gaussian elimination method to obtain the inverse of the transitive matrix. The model also aims at reducing R 0 owning to the fact that when the basic reproduction number is less than 1 infected person, disease dies out and when the reproduction number is greater than 1 infected person, the disease persists. The facts about R 0 geared us to mathematically check for the Routh-Hurwitz stability criteria and Lyapunov Functions to concisely establish the necessary and sufficient conditions for the Local and Global stability of model. results show that, when R 0 < 1 and R 0 > 1 the diseases free equilibrium and endemic equilibrium points are locally and globally asymptotically stable respectively. In order to interpret results and recommend possible control measure of disease, The dynamics of the Quarantine compartment in model was tested via sensitivity analysis to experimentally investigate transition/ transmission pattern. The effect of quarantine analysis on the model shows that preventive measures such as increase in quarantine with treatments during disease outbreak will significantly decrease the Reproduction number. Hence, increase in Quarantine compartment will flatten the curve of (S, I U , I S , I A , Q, R) dynamic model correspondingly.

The Poisson regression is popularly used to model count data. However, real data often do not satisfy the assumption of equality of the mean and variance which is an important property of the Poisson distribution. The Poisson – Gamma (Negative binomial) distribution and the recent Conway-Maxwell-Poisson (COM-Poisson) distributions are some of the proposed models for over- and under-dispersion respectively. Nevertheless, the parameterization of the COM-Poisson distribution still remains a major challenge in practice as the location parameter of the original COM-Poisson distribution rarely represents the mean of the distribution. As a result, this paper proposes a new parameterization of the COM-Poisson distribution via the central location (mean) so that more easily-interpretable models and results can be obtained. The parameterization involves solving nonlinear equations which do not have analytical solutions. The nonlinear equations are solved using the efficient and fast derivative free spectral algorithm. Implementation of the parameterization in R (R Core Team, 2018) is used to present useful numerical results concerning the relationship between the mean of the COM-Poisson distribution and the location parameter in the original COM-Poisson parameterization. The proposed technique is further used to fit COM-Poisson probability models to real life datasets. It was found that obtaining estimates via this parameterization makes the estimation easier and faster compared to directly maximizing the likelihood function of the standard COM-Poisson distribution.