Mathematical analysis of the role of repeated exposure on malaria transmission dynamics

Abstract

This paper presents a deterministic model for assessing the role of repeated exposure on the transmission dynamics of malaria in a human population. Rigorous qualitative analysis of the model, which incorporates three immunity stages, reveals the presence of the phenomenon of backward bifurcation, where a stable diseasefree equilibrium co-exists with a stable endemic equilibrium when the associated reproduction threshold is less than unity. This phenomenon persists regardless of whether the standard or mass action incidence is used to model the transmission dynamics. It is further shown that the region for backward bifurcation increases with decreasing average life span of mosquitoes. Numerical simulations suggest that this region increases with increasing rate of re-infection of first-time infected individuals. In the absence of repeated exposure (re-infection) and loss of infection-acquired immunity, it is shown, using a non-linear Lyapunov function, that International Journal for Theory, Real World Modelling and Simulations 252 A.M. Niger and A.B. Gumel the resulting model with mass action incidence has a globallyasymptotically stable endemic equilibrium when the reproduction threshold exceeds unity.MSC: 92D30, 34D23.

Dynamics of an age-structured two-strain model for malaria transmission

“…The phenomenon of backward bifurcation (where a stable DFE co-exists with a stable endemic equilibrium point when the associate reproduction threshold is less than unity) has been observed in numerous models for disease transmission dynamics (such as those in [8,18,23,[25][26][27]42,50,52,62]). We claim the following result:…”

“…It can be shown, using the approach in Section 3.3.1, that the non-zero equilibria of the low-endemicity model (42) satisfy:…”

“…The low-endemicity model (42) has a unique positive equilibrium ifR L > 1. The non-zero equilibria of the system (23) are called high-endemicity equilibria to distinguish them from the low-endemicity equilibria (where the resistant strain is not transmitted).…”

Qualitative behavior of vector-borne disease model

“…Furthermore, Niger and Gumel [13] investigated the qualitative behavior of malaria model by considering the role of partial immunity. A new mathematical model for malaria was proposed by Wan and Cui [17] by taking into account the partially immune population.…”

Optimal Campaign in Leptospirosis Epidemic by Multiple Control Variables

“…In case of vector born diseases some authors focused on eradication of the disease, by targeting the vector population as a strategy for controlling the disease [15,16] while some scientists studied the effect of vaccinetion on the dynamics of the disease [14]. These scientists believed that optimal control theory is a powerful mathematical tools which make the decision involving complex dynamical systems [17].…”