Dengue fever is a mosquito-borne infectious disease threatening more than a hundred tropical countries of the world. The heterogeneity of mosquito bites of human during the spread of dengue virus is an important factor that should be considered while modeling the dynamics of the disease. However, traditional models assumed homogeneous transmission between host and vectors which is inconsistent with reality. Mathematically, we can describe the heterogeneity and uncertainty of the transmission of the disease by introducing fuzzy theory. In the present work, we study transmission dynamics of dengue with the fuzzy SEIR-SEI compartmental model. The transmission rate and recovery rate of the disease are considered as fuzzy numbers. The dynamical behavior of the system is discussed with different amounts of dengue viruses. Also, the fuzzy basic reproduction number for a group of infected individuals with different virus loads is calculated using Sugeno integral. Simulations are made to illustrate the mathematical results graphically.

Malaria is one of the most common mosquito borne diseases. Temperature is an important factor which affects the life cycle of the mosquitoes and transmission dynamics of the malaria disease. In the present work, we use SEIR compartmental model for the human population and LSEI compartmental model for mosquito population taking temperature dependent parameters. Basic reproduction number, R 0 of the model is computed using Next Generation Matrix Method. Stability of the disease free equilibrium and the existence of the endemic equilibrium point are discussed by basic reproduction number, R 0. Numerical results are carried out with different temperature levels. It is observed that temperature affects the transmission dynamics of malaria disease significantly.

Corona Virus Disease (COVID-19) is an infectious disease caused by severe acute respiratory syndrome corona virus 2 (SARS-CoV-2). The virus is spread between people during close contact via small droplets produced by coughing, sneezing, talking etc. In the present work, the transmission dynamics of the COVID- 19 is studied using SEIHR epidemic compartmental model. Basic reproduction number is computed with the help of the method of Next Generation Matrix. Stability of equilibrium points of the model is discussed. Sensitivity analysis of the model is performed to determine the relative importance of the model parameters. Simulations are made to illustrate the mathematical results graphically.

Dengue is one of the most serious mosquito-borne infectious diseases in the world. The number of dengue cases is increasing every year worldwide. In this work, we discuss the fuzzy epidemic SEIR-SEI compartmental model with the intervention of bed nets and fumigation to describe the transmission dynamics of dengue disease. We consider the biting rate, transmission rate, and recovery rate of the disease as fuzzy numbers. With different amounts of virus loads, we discuss the dynamical behavior of the system. The sensitivity analysis of the model is performed to compare the relative importance of the model parameters and to discuss the importance of fumigation, use of bed nets, and the effectiveness of bed nets. We demonstrate the bifurcation of the equilibrium point of the system with and without fumigation, with and without bed net user, and with different levels of effectiveness of bed nets. Numerical simulations are made to illustrate the mathematical results graphically. The infectivity of the disease depends on the amount of virus loads. The mathematical and simulated result shows that the intervention strategies, use of fumigation and bed nets, reduces the value of the basic reproduction number. Thus, this study suggests that the endemic situation of the disease can be brought under control by the effective use of the combination of fumigation and bed nets.