In this paper a mathematical model of monkey pox virus transmission dynamics with two interacting host populations; humans and rodents is formulate. The quarantine class and public enlightenment campaign parameter are incorporated into human population as means of controlling the spread of the disease. The Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) are obtained. The basic reproduction number are computed and used for the analysis. The Disease Free Equilibrium (DFE) is analyzed for stability using Jacobian matrix techniques and Lyapunov function. Stability analysis shows that the DFE is stable if. th th
In this paper, mathematical model of Monkey-Pox transmission is developed and investigated, using ordinary differential equation. We verified the feasible region of the model and showed the positivity of the solutions. We obtained the disease free equilibrium (DFE). We computed and analysed the effective basic reproduction number () of the model.
Acute diarrhea disease has a greater threat to human population especially in poor sanitary or hygienic environments, which caused enormous mortality and mobility in the Society. In this paper, we proposed a model to describe the transmission of the acute diarrhea disease and optimal control strategies in a community. The reproduction number and global dynamics of the model are obtained. Global Stability of the Disease free and endemic state of the model equations is determined. It was found that, the Disease Free Equilibrium is globally asymptotically stable in feasible region Ω if R0≤1 and Endemic state is globally asymptotically stable when R0>1. The Optimal control problem is designed with two control strategies, namely, the prevention through minimizing the contact between the infected with acute diarrhea infectious and susceptible, and treatment of an individual. The existence of optimal control model is obtained. Numerical results of the dynamics of the disease are presented. It was found that, as the effective contact rate increases, it increases the reproduction number of the model equations, also as the effectiveness of compliance of good hygiene increases, it decreases the reproduction number of the model by varying the contact rate and more so, as production rate of acute diarrhea bacteria increases, it increases the secondary cases of the infected individuals.
In this paper, we present a deterministic model on the transmission dynamics of Lymphatic Filariasis.Non-Standard Finite Difference Method (NSFDM) is employed to attempt the solution of the model. The validity of the NSFDM in solving the model is established by using the computer in-built classical fourth-order Runge-Kutta method. The comparism between Non-Standard Finite Difference Method solution and Runge-Kutta (RK4) were performed which were found to be efficient, accurate and rapidly convergence.
A mathematical model of the co-infection dynamics of malaria and dengue fever condition is formulated. In this work, the Basic reduction number is computed using the next generation method. The diseasefree equilibrium (DFE) point of the model is obtained. The local and global stability of the disease-free equilibrium point of the model is established. The result show that the DFE is locally asymptotically stable if the basic reproduction number is less than one but may not be globally asymptotically stable.
Keywords: Malaria; Dengue Fever; Co-infection; Basic reproduction number; Disease-Free equilibrium
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