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

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