Mathematical analysis of mosquito population global dynamics using delayed-logistic growth

Abstract

Malaria is a major public health issue in many parts of the world, and the anopheles mosquitoes which drive transmission are key targets for interventions. Consequently, a best understanding of mosquito populations dynamics is necessary in the fight against the disease. Hence, in this paper we propose a delayed mathematical model of the life cycle of anopheles mosquitoes by using delayed-logistic population growth. The model is formulated by inserting the time delay into the logistic population growth rate, that accounts for the period of growth from eggs to the last aquatic stage, which is pupae. Depending on the system parameters, we establish a threshold for survival and extinction of the anopheles mosquitoes population. Moreover, by choosing the time delay as a bifurcation parameter, we prove that the system loses its stability and a Hopf bifurcation occurs when time delay passes through some critical values. Finally, we perform some numerical simulations and the results are well in keeping with the analytical analysis.

Optimal control analysis of a COVID-19 and Tuberculosis (TB) co-infection model with an imperfect vaccine for COVID-19

“…The DFE of model ( 5 ), denoted by is given by: As in the previous section, we have Thus, we established the following result thanks to Theorem 2 in Driessche and Watmough [ 13 , 23 , 26 , 32 , 51 ].…”

“…Based on all the information given above, we draw the compartmental representation given in Fig. 1 , from which, we obtain the following model ( 2 ) of the transmission dynamics of COVID-19 and TB co-infection in a population: with positive initial conditions [ 1 , 23 , 33 , 45 ], i.e. Now, we will show that model ( 2 ) is epidemiologically well-posed.…”

Mathematical analysis of the impact of the media coverage in mitigating the outbreak of COVID-19

“…More precisely, in this section, we proved the well-posedness of the model, we computed the disease-free equilibrium point and the basic reproduction number that has been shown to be the key threshold parameter in investigating the disease dynamics. Moreover, thanks to certain conditions on , to the Routh–Hurwitz criterion and to Lyapunov’s function principle [29] , [30] , [32] , we have studied the local and global stabilities of the steady states. The sensitivity of to the various parameters that compose it and herd immunity were studied in Section 4 .…”