Mathematical modelling for the transmission dynamics of Rift Valley fever virus with human host

Rift Valley Fever (RVF) is a viral zoonosis spread primarily by mosquitos that primarily affects livestock but has the potential to affect humans. Because of its potential to spread quickly and become an epidemic, it has become a public concern. In this article, the transmission dynamics of RVF with mosquito, livestock and human host using a compartmental model is studied and analyzed. The basic reproduction number R0 is computed using next generation matrix and the disease-free equilibrium state is found to be locally asymptotically stable if R0 1 which implies that rift valley fever could be put under control in a population where the reproduction number is less than 1. The numerical simulations give insightful results to further explore the dynamics of the disease based on the effect of three interventions; efficacy of vaccination, culling of livestock and trapping of mosquitoes introduced in the model

UNCERTAIN CONTROLLABILITY AND OBSERVABILITY OF AN OPTIMAL CONTROL MODEL

The interest of this paper is to examine the controllability and observ- ability of control system in the con�guration state-space of uncertain optimal con- trol system. The control system is designed based on the realization of capital asset values where a special case of asset management is modelled and optimized. Thus some necessary and su�cient conditions of the controllability and observability of the deterministic systems and the corresponding uncertain systems for the case of uncertain optimal control system with application in capital asset management is considered

Optimal Intervention Strategies for Transmission Dynamics of Cholera Disease

In this paper, an optimal control model for cholera disease described by a system of first order ordinary differential equations was formulated and examined. The necessary conditions for the attainment of optimum level of control in the dynamical system were derived by employing the Pontryagin’s Maximum principle. Numerical studies of the analytical results were conducted to investigate the behaviour of the optimality system and the results were tabulated. The tabular results showed that the combination of the interventions up to 80% was capable of bringing cholera epidemic under control. As the rate of control was directly related to the cost of control, the result of the analysis revealed the control outlay that maintained the optimum balance of interventions with the lowest cost.

Differential Transform Method for Solving Mathematical Model of SEIR and SEI Spread of Malaria

In this paper, we use Differential Transformation Method (DTM) to solve two dimensional mathematical model of malaria human variable and the other variable for mosquito. Next generation matrix method was used to solve for the basic reproduction number  and we use it to test for the stability that whenever  the disease-free equilibrium is globally asymptotically stable otherwise unstable. We also compare the DTM solution of the model with Fourth order Runge-Kutta method (R-K 4) which is embedded in maple 18 to see the behaviour of the parameters used in the model. The solutions of the two methods follow the same pattern which was found to be efficient and accurate

Transmission Dynamics of Fractional Order Brucellosis Model Using Caputo–Fabrizio Operator

In this paper, a noninteger order Brucellosis model is developed by employing the Caputo–Fabrizio noninteger order operator. The approach of noninteger order calculus is quite new for such a biological phenomenon. We establish the existence, uniqueness, and stability conditions for the model via the fixed-point theory. The initial approachable approximate solutions are derived for the proposed model by applying the iterative Laplace transform technique. Finally, numerical simulations are conducted for the analytical results to visualize the effect of various parameters that govern the dynamics of infection, and the results are presented using plots

A fractional derivative modeling study for measles infection with double dose vaccination

This study proposes a novel mathematical framework to study the spread dynamics of diseases. A measles model is developed by dividing the vaccinated compartment into the vaccinated-with-the-first-dose and the-second-dose populations. The model parameters are estimated using the genetic algorithm for measles transmission based on monthly cumulative measles data in Indonesia. The threshold is determined to measure a population’s potential spread of measles. The stability of the equilibria is investigated, and the sensitivity analysis is then presented to find the most dominant parameter on the spread of measles. We extend the classical model into Atangana–Baleanu Caputo (ABC) derivative and consider the effects of the first and second vaccination doses on susceptible and exposed individuals. These outcomes are based on the different fractional parameter values and can be utilized to identify significant disease-control strategies. The yields are graphically exhibited to support our results. The overall finding suggests that taking preventive measures has a significant influence on limiting the spread of measles in the population. Increasing vaccination coverage, in particular, will reduce the number of infected individuals, thereby lowering the disease burden in the population

Fractional-order modelling and analysis of diabetes mellitus: Utilizing the Atangana-Baleanu Caputo (ABC) operator

This article aims to introduce and analyze a diabetes mellitus model of fractional order, utilizing the ABC derivative. Diabetes mellitus is a prevalent and significant disease worldwide, ranking among the top causes of mortality. It is characterized by chronic metabolic dysfunction, leading to elevated blood glucose levels and subsequent damage to vital organs including the nerves, kidneys, eyes, blood vessels, and heart. The fractional ABC derivative is used in this study to describe and analyze diabetes mellitus mathematically while removing hereditary influences. The investigation begins by exploring the initial points of the diabetes mellitus model. Under the fractional ABC operator, Picard's theorem is used to prove the existence and uniqueness of solutions. For the numerical approximation of solutions in the fractional-order diabetes mellitus model, this study used a specialized technique that combines the principles of fractional calculus and a two-step Lagrange polynomial interpolation. Finally, the obtained results are visually presented through graphical representations, serving as empirical evidence to support our theoretical findings. The numerical experiments showed that the proportion of patients with diabetes mellitus increased as the fractional dimension (θ) reduced. The combination of mathematical modelling, analysis, and numerical simulations provides insights into the dynamics of diabetes mellitus, offering valuable contributions to the understanding and management of this prevalent disease. Additionally, the proposed scheme can be enhanced by incorporating the ABC operator, allowing for the simulation of real-world dynamics and behavior in the coexistence of diabetes mellitus and tuberculosis