A bio-mathematical approach to control the Anopheles mosquito using sterile males technology

Initiative for this study is taken to solve the mathematical model which is base-forming with population dynamics of the Anopheles mosquito using an advanced computational intelligence scheme named as genetic algorithm (GA), artificial neural network (ANN). This ANN is a famous global search method, active set (AS) scheme known as a quick local refinement, i.e. ANN-GA-AS. An error-based fitness function is optimized which is made by using the sense of the differential system and boundary conditions for solving the Anopheles mosquito control model. The ability of the stochastic ANN-GA-AS approach to solve the population dynamics of the Anopheles mosquito is examined to check the exactness, efficiency, precision, and consistency of the scheme. The numerical outcomes of the Anopheles mosquito control model through the ANN-GA-AS approach are compared with the reference Adams numerical results to show the significance of the designed scheme. Moreover, statistical considerations using the “semi-interquartile range”, “Theil’s inequality coefficient”, and “mean absolute deviation” have been applied to validate the precision and accuracy of the obtained results.

Stability behavior of a two-susceptibility SHIR epidemic model with time delay in complex networks

Taking two susceptible groups into account, we formulate a modified subhealthy-healthy-infected-recovered (SHIR) model with time delay and nonlinear incidence rate in networks with different topologies. Concretely, two dynamical systems are designed in homogeneous and heterogeneous networks by utilizing mean field equations. Based on the next-generation matrix and the existence of a positive equilibrium point, we derive the basic reproduction numbers R 0 1 and R 0 2 which depend on the model parameters and network structure. In virtue of linearized systems and Lyapunov functions, the local and global stabilities of the disease-free equilibrium points are, respectively, analyzed when R 0 1 < 1 in homogeneous networks and R 0 2 < 1 in heterogeneous networks. Besides, we demonstrate that the endemic equilibrium point is locally asymptotically stable in homogeneous networks in the condition of R 0 1 > 1 . Finally, numerical simulations are performed to conduct sensitivity analysis and confirm theoretical results. Moreover, some conjectures are proposed to complement dynamical behavior of two systems.

Stochastic dynamics of the transmission of Dengue fever virus between mosquitoes and humans

Considering the impact of environmental white noise on the quantity and behavior of vector of disease, a stochastic differential model describing the transmission of Dengue fever between mosquitoes and humans, in this paper, is proposed. By using Lyapunov methods and Itô’s formula, we first prove the existence and uniqueness of a global positive solution for this model. Further, some sufficient conditions for the extinction and persistence in the mean of this stochastic model are obtained by using the techniques of a series of stochastic inequalities. In addition, we also discuss the existence of a unique stationary distribution which leads to the stochastic persistence of this disease. Finally, several numerical simulations are carried to illustrate the main results of this contribution.

Global analysis of a reaction–diffusion blood-stage malaria model with immune response

Malaria is one of the most dangerous diseases that threatens people’s lives around the world. In this paper, we study a reaction-diffusion model for the within-host dynamics of malaria infection with an antibody immune response. The model is given by a system of partial differential equations (PDEs) to describe the blood-stage of malaria life cycle. It addresses the interactions between uninfected red blood cells, antibodies, and three types of infected red blood cells, namely ring-infected red blood cells, trophozoite-infected red blood cells and schizont-infected red blood cells. Moreover, the model contains a parameter to measure the efficacy of isoleucine starvation and its effect on the growth of malaria parasites. We show the basic properties of the model. We compute all equilibria and derive the thresholds from the conditions of existence of malaria equilibrium points. We prove the global stability of all equilibrium points based on choosing suitable Lyapunov functionals. We use the characteristic equations to verify the local instability of equilibrium points. We finally execute numerical simulations to validate the theoretical results and highlight some important observations. The results indicate that isoleucine starvation can have a critical impact on the stability of equilibrium points. When the efficacy of isoleucine starvation is high, it switches the system from the infection state to the malaria-free state. The presence of an antibody immune response does not lead to the elimination of malaria infection, but it suppresses the growth of malaria parasites and increases the amount of healthy red blood cells.