Mathematical modeling of the dynamics of vector-borne diseases transmitted by mosquitoes : taking into account aquatic stages and gonotrophic cycle

Abstract

In this paper, we formulate a mathematical model of vector-borne disease dynamics. The model is constructed by considering two models : a baseline model of vector population dynamics due to Lutambi et al. that takes into account the development of the aquatic stages and the female mosquitoes gonotrophic cycle and an SI-SIR model describing the interaction between mosquitoes and human hosts. We briefly study the baseline model of vectors dynamics and, for the transmission model, we explicitly compute the equilibrium points, and by using the method of Van den Driesshe and J. Watmough, we derive the basic reproduction number ℛ0. Otherwise, thanks to Lyapunov’s principle, Routh-Hurwitz criteria and a favorable result due to Vidyasagar, we establish the local and global stability results of the equilibrium points. Furthermore, we establish an interesting relationship between the mosquito reproduction number ℛ v and the basic reproduction number ℛ0. It then follows that aquatic stages and behavior of adult mosquitoes have a significant impact on disease transmission dynamics. Finally, some numerical simulations are carried out to support the theoretical findings of the study.

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

“…We can also prove, using similar contradictions, that the other state variables are positive [ 11 , 14 , 22 , 45 , 47 ].…”

“…Suppose now that we then have i.e In this case the population is decreasing and since the domain is compact, thus all the solutions remain there, [ 11 , 26 , 39 , 40 , 46 ]. …”

A Complex Dynamic of an Eco-Epidemiological Mathematical Model with Migration

“…Therefore, the transversality condition hold. Thus, Hopfbifurcation occurs at m 1 ¼ m cr for system (2) around the coexistence equilibrium E 3 : □ Now, let us investigate the global stability of the coexistence equilibrium point [12,26,[29][30][31][32].…”

Mathematical Modeling and its Stability Analysis of an SEIR Model to Control Dengue by Segregating the Infective: An Approach for Efficient Resource Allocation

“…µ(γ+ω+µ)(η 1 +η 2 +δ 1 +k 1 +µ) which is obtained from Equation (9). By the definition of normalised forward sensitivity index of R 0 , the sensitivity indices can be simulated as given below…”

“…The study of risk factors involved in a disease is necessary in order to analyse the outbreak (8) . Especially regarding dengue transmission, it is imperative to comprehend the dynamics of vector-borne diseases (9) . To address this need, a study conducted in Bangladesh (10) introduced a model that accounts for both host and vector population involved in dengue transmission.…”