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... Multiple researchers have made significant efforts to understand the dynamics of T. gondii disease. Other relative studies can be found in [32][33][34]. ...
Toxoplasmosis is a significant zoonotic disease that poses risks to public health and animal health, making the understanding of its transmission dynamics crucial. In this study, we present a novel fractional-order model that captures complex interactions among human, cat, and mouse populations, providing deeper insights into the disease spread and control. We utilize mathematical techniques to analyze the model properties, including the existence, uniqueness, positivity, and boundedness of solutions, along with stability analysis of the equilibrium states. The basic reproduction number is derived, revealing the threshold for potential outbreaks. Our findings indicate that key parameters significantly influence the dynamics of toxoplasmosis, with implications for targeted intervention strategies. We propose the QLM-FONP numerical scheme for efficient resolution of the model and provide a comprehensive convergence analysis, demonstrating the reliability of the numerical solutions. The results confirm the effectiveness of our approach, illustrating that the proposed model not only offers accurate predictions but also extends beyond previous efforts in the literature by incorporating fractional-order dynamics, which better reflect real-world transmission processes. Overall, this study enhances the understanding of toxoplasmosis transmission and informs future research and control efforts.
... On the other hand, there is a possibility for the mechanism to be ineffective so that all the compartments are non-empty. The former situation relates to disease-free equilibrium (DFE) while the latter relates to endemic equilibrium (EE) in epidemic modeling (Ayoade & Ibrahim, 2022b;Ayoade et al., 2023a;Ayoade et al., 2023b;Adeyemo & Ayoade, 2023). ...
A certificate is evidence of participating in a process, and anyone who holds a certificate is believed to have the prerequisites necessary to handle what the certificate qualifies them for. However, this perception might be incorrect if the certificate has been obtained by taking shortcuts. [Objective] In this paper, a compartmental model was developed to quantify factors that could put the authenticity of a certificate in doubt by examining the trade-off between academic standards and failure rates in the context of tertiary education institutions in Nigeria. [Methodology] The model was validated using several mathematical theorems. Equilibria for the model and the threshold for acceptable academic performance were derived. Stability analysis was carried out by using the stability theory of differential equations based on the derived acceptable academic performance threshold. [Results] The theoretical results for the model were validated through numerical simulations, and the results from the simulations linked acceptable failure rates to academic performance falling below the threshold of the institutions’ standards. [Conclusions] The policy implication of the result is that an increase in the supply of qualified graduates into Nigeria’s labor markets, as well as a reduction in the rate of unemployment, is a function of maintaining academic standards.
... Following [31,9], the equation for changes in diabetics population who have become critically disabled (i.e. A(t)) can be neglected from the analysis. ...
Diabetes mellitus is a global health problem, escalating at a disturbing rate due to unbalanced lifestyles and some underlying health issues. In this work, a system of first-order linear ordinary differential equations as well as numerical simulations were employed to gain insight into the dynamics of the disease. The theoretical outcome of the analysis was derived in terms of the model parameters while computer simulation was used to assess the behaviour of the model in terms of the parameters values. Both the theoretical and numerical studies of the model revealed lifestyles and effective treatment as the parameters to be targeted for effective reduction in both diabetes prevalence and mortality. It is therefore concluded that diabetes prevalence and mortality reduction is a function of adjustment in unbalanced lifestyles as well as improvement in diabetes treatment.
... A parameter is said to be sensitive if a little change in its value results in a significant change in how the differential equations are solved. To study a change in the model's solution with regard to a certain parameter, the derivative of the solution for the parameter is utilized [12]. We compute the sensitivity indices of the key parameters following the normalised forward sensitivity index approach [9] thus ...
Lassa fever is a deadly viral disease whose incubation period ranges from six to twenty-one days and about eighty percent of Lassa virus infection is asymptomatic. A deterministic model was formulated to quantify the transmission dynamics of the disease under isolation and treatment of the isolated asymptomatic and symptomatic humans for effective management and possible elimination of the disease. The solutions of the model were shown to be positive and bounded. Equilibrium analysis was conducted and both the disease-free and the endemic equilibria were derived. The threshold quantity for disease elimination , , was also obtained and used to derive conditions for the existence of stability of the eqilibria. The quantity was also employed to examine the sensitivity of the model parameters to disease propagation and reduction. The theoretical analysis was then complemented with the quantitative analysis by adopting a set of realistic values for the model parameters in order to show the effect of isolation and treatment on the spread and fatality of Lassa fever. Results from the quantitative study showed that death and infection from Lassa fever fell continuously as more and more exposed individuals were detected and isolated for treatment. The study therefore suggested that any measure taken to eradicate or curtail Lassa fever spread should include detection and isolation of the exposed humans for prompt treatments.