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

Multi-step Homotopy Analysis Method for Solving Malaria Model

In this paper, we consider the modified epidemiological malaria model proposed by Abadi and Harald. The multi-step homotopy analysis method (MHAM) is employed to compute an approximation to the solution of the model of fractional order. The fractional derivatives are described in the Caputo sense. We illustrated the profiles of the solutions of each of the compartments. Figurative comparisons between the MHAM and the classical fourth-order reveal that this method is very effective

APPROXIMATE SOLUTION TO FRACTIONAL ORDER SOIL TRANSMITTED HELMINTH INFECTION MODEL USING LAPLACE ADOMIAN DECOMPOSITION METHOD

In this study, we proposed a fractional order compartmental model based on the Caputo derivative to describe the dynamics of soil-transmitted helminth infection. We employed the Laplace Adomian Decomposition Method (LADM) to derive series solutions for each equation within the system of non-linear differential equations that comprise the epidemiological model. Our findings indicate that the infinite series generated by LADM converges to the exact solution of the system. We performed numerical simulations of the fractional order compartmental deterministic model using MATLAB to validate the approximate results. Additionally, comparing the solutions of the fractional order model with the classical model reveals that the fractional order model offers greater flexibility, allowing the system to be adjusted to achieve various desired outcomes in different compartments by varying the fractional order to values such as 0.75, 0.8, 0.85, 0.9, 0.95, and 1

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

Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate

COVID-19 pandemic represents an unprecedented global health crisis which has an enormous impact on the world population and economy. Many scientists and researchers have combined efforts to develop an approach to tackle this crisis and as a result, researchers have developed several approaches for understanding the COVID-19 transmission dynamics and the way of mitigating its effect. The implementation of a mathematical model has proven helpful in further understanding the behaviour which has helped the policymaker in adopting the best policy necessary for reducing the spread. Most models are based on a system of equations which assume an instantaneous change in the transmission dynamics. However, it is believed that SARS-COV-2 have an incubation period before the tendency of transmission. Therefore, to capture the dynamics adequately, there would be a need for the inclusion of delay parameters which will account for the delay before an exposed individual could become infected. Hence, in this paper, we investigate the SEIR epidemic model with a convex incidence rate incorporated with a time delay. We first discussed the epidemic model as a form of a classical ordinary differential equation and then the inclusion of a delay to represent the period in which the susceptible and exposed individuals became infectious. Secondly, we identify the disease-free together with the endemic equilibrium state and examine their stability by adopting the delay differential equation stability theory. Thereafter, we carried out numerical simulations with suitable parameters choice to illustrate the theoretical result of the system and for a better understanding of the model dynamics. We also vary the length of the delay to illustrate the changes in the model as the delay parameters change which enables us to further gain an insight into the effect of the included delay in a dynamical system. The result confirms that the inclusion of delay destabilises the system and it forces the system to exhibit an oscillatory behaviour which leads to a periodic solution and it further helps us to gain more insight into the transmission dynamics of the disease and strategy to reduce the risk of infection

A fractional-order mathematical model for malaria and COVID-19 co-infection dynamics

This study proposes a fractional-order mathematical model for malaria and COVID-19 co-infection using the Atangana–Baleanu Derivative. We explain the various stages of the diseases together in humans and mosquitoes, and we also establish the existence and uniqueness of the fractional order co-infection model solution using the fixed point theorem. We conduct the qualitative analysis along with an epidemic indicator, the basic reproduction number R0 of this model. We investigate the global stability at the disease and endemic free equilibrium of the malaria-only, COVID-19-only, and co-infection models. We run different simulations of the fractional-order co-infection model using a two-step Lagrange interpolation polynomial approximate method with the aid of the Maple software package. The results reveal that reducing the risk of malaria and COVID-19 by taking preventive measures will reduce the risk factor for getting COVID-19 after contracting malaria and will also reduce the risk factor for getting malaria after contracting COVID-19 even to the point of extinction