The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss

Abstract

Abstract:In this paper, a compartment model has been built, presented and investigated the dynamics and spread of zika virus in both human and mosquito populations. It is focused to study the impact of symptomatic and asymptomatic infective immigrants on the spread of zika virus. A new mathematical model for human and model for vector population has been designed and presented. Here is symptomatic infective and is asymptomatic infective human populations. The present model is developed making some reasonable modifications in the corresponding epidemic model by considering symptomatic and asymptomatic infective immigrants. Susceptible vectors get infection either from symptomatic or asymptomatic infected human populations. The basic reproduction number is derived using the next generation matrix method. Disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if the reproduction number takes a value less than one unit and unstable if it is more than one unit. Simulation study is conducted using MATLAB ode45.

The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study

“…The spread of the disease modeled using ordinary deferential equations ODEs where humans interact and infect each other [1,12,16]. The major application of these equations is when the rate of change of a variable is related to other variables, as it is so in most physical and biological systems.…”

“…Many powerful mathematical tools exist for the analysis and numerical solution of models based on deferential equations [1]. Many mathematical models did not consider symptomatic and asymptomatic infected immigrants and self isolation techniques on the dynamics of infectious disease [16].…”

“…Disease-free equilibrium (DFE) points are steady-state solutions where there is no corona virus infection and the equilibrium points are obtained by setting the right hand sides of the model equations to zero [12,16]. Disease free equilibrium points are steady state solutions of the system of ODE in the absence of disease in the population.…”

“…The impact of migration of population on the distribution and spread of disease is required to be analyzed properly and must be understood clearly [7]. Migration and immigration of the people from one country to another country due to deferent reasons play a crucial role in the evolution and spread of infectious disease [16]. The models published thus far have not taken into account the role of exposed and infected immigrants as well as the role of self isolation from the virus in the transmission of COVID−19.…”

Modified Model and Stability Analysis of the Spread of Hepatitis B Virus Disease

“…The basic reproduction number is defined as the effective number of secondary infections caused by typical infected individual during his entire period of infectiousness [11]. The basic reproductive number for the general model (1) to (5) can be determined using the next generation matrix method [12].…”