Jean M. Tchuenche

Optimal Control and Sensitivity Analysis of an Influenza Model with Treatment and Vaccination

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin’s maximum principle, and it is observed that full treatment effort should be given while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point.

A Mathematical Model of Rift Valley Fever with Human Host

Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold

Dynamics of fisheries with prey reserve and harvesting

\mathcal{R}_0

HIV/AIDS MODEL ASSESSING THE EFFECTS OF GENDER-INEQUALITY AFFECTING WOMEN IN AFRICAN HETEROSEXUAL SETTINGS

is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission

STUDYING THE IDENTIFIABILITY OF EPIDEMIOLOGICAL MODELS USING MCMC

\mathcal{R}_0

Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics

and the endemic equilibrium are determined. Both