Mathematical Modeling and Stability Analyses of Lassa Fever Disease with the Introduction of the Carrier Compartment

In this paper, a new mathematical model which takes into account the human and vector populations together with their interactions during Lassa fever disease transmission was developed. This transmission process is denoted by a seven mutually exclusive compartments for the human and vector populations. The proposed model is used to introduce the incubation period of the disease, a period in which an infected individual is yet to be symptomatic but infectious however, as denoted by the carrier human compartment. This carrier compartment was critically examined for its short and long term effects on the spread and control of the disease. Local and global stability analyses of the equilibrium points of the model was carried out using the first generation matrix approach and the direct Lyapunov method respectively. These analyses showed that the disease free equilibrium point of the developed model is locally asymptotically stable but not globally asymptotically stable. It was also observed that, although, there exist a unique endemic equilibria for the disease, this equilibria however is not stable. Numerical simulations of the model were carried out by implementing the MATLAB ODE45 algorithm for solving non-stiff ordinary differential equations. The results of these simulations are the effects of the various model parameters on each compartment of the developed model. Based on the findings of this research, necessary recommendations were made for the applications of the model to an endemic area. Keywords: Mathematical Model, Stability Analyses, Lassa Fever, Equilibrium Points, Numerical Simulation. DOI: 10.7176/MTM/9-6-04 Publication date: June 30th 201

Stability Analysis Using Nonstandard Finite Difference Method and Model Simulation for Multi-Mutation and Drug Resistance with Immune-Suppression

We introduced recently a model that takes into account multi-mutation and drug resistance of tumor cells in a case of simple immune system and immune-suppression caused by the resistant tumor cells. The present study is to apply the Nonstandard finite difference method to that model we recently developed in analyzing the stability of non-tumor states to identify under which conditions tumor can be eliminated in the presence of both immunotherapy and chemotherapy. Numerical simulations of the model in the presence of both immunotherapy and chemotherapy are performed with the aid of MATLAB software using ode45 function and under different treatment strategies to analyze the behavior of both the tumor and immune system cells. The findings of this study indicate that tumor cells can be only eliminated under certain conditions, when a second specific chemotherapy drug that is only toxic to resistant tumor cells is introduced. Moreover, it gives an insight into how tumor and immune system cells evolve when the dynamical system conveys both inherent and drug-induced resistance with immune-suppression, in the presence of both immunotherapy and chemotherapy. Treatment strategies effective are proposed in this case. Keywords: Cancer modeling, Drug resistance, Mutation, Immune system, Immunotherapy, Immune-Suppression, Chemotherapy, Nonstandard finite difference method / scheme. AMS Subject Classifications: 37C75; 65L12; 92C37; 68U20