Abstract

In this paper, a new mathematical model which takes into account the human and vector populations together with their interactions during Lassa fever disease transmission was developed. This transmission process is denoted by a seven mutually exclusive compartments for the human and vector populations. The proposed model is used to introduce the incubation period of the disease, a period in which an infected individual is yet to be symptomatic but infectious however, as denoted by the carrier human compartment. This carrier compartment was critically examined for its short and long term effects on the spread and control of the disease. Local and global stability analyses of the equilibrium points of the model was carried out using the first generation matrix approach and the direct Lyapunov method respectively. These analyses showed that the disease free equilibrium point of the developed model is locally asymptotically stable but not globally asymptotically stable. It was also observed that, although, there exist a unique endemic equilibria for the disease, this equilibria however is not stable. Numerical simulations of the model were carried out by implementing the MATLAB ODE45 algorithm for solving non-stiff ordinary differential equations. The results of these simulations are the effects of the various model parameters on each compartment of the developed model. Based on the findings of this research, necessary recommendations were made for the applications of the model to an endemic area. Keywords: Mathematical Model, Stability Analyses, Lassa Fever, Equilibrium Points, Numerical Simulation. DOI : 10.7176/MTM/9-6-04 Publication date : June 30 th 2019

Highlights

  • Lassa Fever (LF) is a fatal acute Viral Hemorrhagic fever caused by Lassa Virus (LASV)

  • In contrast with some other viral diseases, such as the Human Immune-deficiency virus (HIV), of which the Center for Disease Control and Prevention, [9], states that it cannot be transmitted via water, saliva, tears, or sweat, due to its very short lifespan outside the host, LASV, according to the Pathogen Safety Data Sheet, [22], is stable as an aerosol and has a biological half-life, between 240C and 320C, of 10.1 to 54.6 minutes outside host

  • The results of the analyses of the developed model indicate that the disease free equilibrium of Lassa fever is stable while the endemic equilibrium point is unstable

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Summary

Introduction

Lassa Fever (LF) is a fatal acute Viral Hemorrhagic fever caused by Lassa Virus (LASV). In contrast with some other viral diseases, such as the Human Immune-deficiency virus (HIV), of which the Center for Disease Control and Prevention, [9], states that it cannot be transmitted via water, saliva, tears, or sweat, due to its very short lifespan outside the host, LASV, according to the Pathogen Safety Data Sheet, [22], is stable as an aerosol and has a biological half-life, between 240C and 320C, of 10.1 to 54.6 minutes outside host This implies that contact with the secretions of an infected rodent or human over this period of time could still lead to the virus been transmitted. [15] investigated the prevalence of LF disease in Northern part of Edo State, Nigeria with a high rate of infection on contact persons The results of their investigations showed that, to control the spread of the virus, the average number of new secondary infection(s) generated by a single infected individual/rodent during their infectious period, R0, must be brought below one. (βc Ch βhIh βv Iv )Sh μhSh dCh dt σhCh γ1Ch δhCh μhCh dIh dt σh Ch γ2Ih γ4Ih δh Ih μhIh dTh dt βγ3Th

The Invariant Region
Positivity of the Solution The Positivity Theorem
The Endemic Equilibrium Point
Local Asymptotic Stability Analysis
Global Asymptotic Stability Analysis
Infected Vector Population
Conclusion and Recommendations
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