arXiv subjects

Jean Claude Kamgang

Publications and source records attributed to Jean Claude Kamgang.

3 recordsLinked to original sources

arXiv2023

Analysis of Control Measures for Vector-borne Diseases Using a Multistage Vector Model with Multi-Host Sub-populations

We propose and analyze an epidemiological model for vector borne diseases that integrates a multi-stage vector population and several host sub-populations which may be characterized by a variety of compartmental model types: subpopulations all include Susceptible and Infected compartments, but may or may not include Exposed and/or Recovered compartments. The model was originally designed to evaluate the effectiveness of various prophylactic measures in malaria-endemic areas, but can be applied as well to other vector-borne diseases. This model is expressed as a system of several differential equations, where the number of equations depends on the particular assumptions of the model. We compute the basic reproduction number $\mathcal R_0$, and show that if $\mathcal R_0\leqslant 1$, the disease free equilibrium (DFE) is globally asymptotically stable (GAS) on the nonnegative orthant. If $\mathcal R_0>1$, the system admits a unique endemic equilibrium (EE) that is GAS. We analyze the sensitivity of $R_0$ and the EE to different system parameters, and based on this analysis we discuss the relative effectiveness of different control measures.

q-bio.PE↗

arXiv2018

Analysis of Malaria Control Measures Effectiveness Using Multi-Stage Vector Model

We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in malaria-endemic areas. The mathematical model consists of a system of several ordinary differential equations, and is based on a multicompartment representation of the system. The model takes into account the mutliple resting-questing stages undergone by adult female mosquitos during the period in which they function as disease vectors. We compute the basic reproduction number $\mathcal R_0$, and show that that if $\mathcal R_0<1$, the disease free equilibrium (DFE) is globally asymptotically stable (GAS) on the non-negative orthant. If $\mathcal R_0>1$, the system admits a unique endemic equilibrium (EE) that is GAS. We perform a sensitivity analysis of the dependence of $\mathcal R_0$ and the EE on parameters related to control measures, such as killing effectiveness and bite prevention. Finally, we discuss the implications for a comprehensive, cost-effective strategy for malaria control.

q-bio.PE↗

arXiv2015

Backward Bifurcation and Control in Transmission Dynamics of Arboviral Diseases

In this paper, we derive and analyze a compartmental model for the control of arboviral diseases which takes into account an imperfect vaccine combined with individual protection and some vector control strategies already studied in the literature. After the formulation of the model, a qualitative study based on stability analysis and bifurcation theory reveals that the phenomenon of backward bifurcation may occur. The stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the reproduction number, R 0 , is less than unity. Using Lyapunov function theory, we prove that the trivial equilibrium is globally asymptotically stable; When the disease-- induced death is not considered, or/and, when the standard incidence is replaced by the mass action incidence, the backward bifurcation does not occur. Under a certain condition , we establish the global asymptotic stability of the disease--free equilibrium of the full model. Through sensitivity analysis, we determine the relative importance of model parameters for disease transmission. Numerical simulations show that the combination of several control mechanisms would significantly reduce the spread of the disease, if we maintain the level of each control high, and this, over a long period.

math.DS↗