Abstract
Rift Valley fever is a zoonotic disease which is mainly transmitted by mosquitoes and has potential to affect humans and animals. To gain some understanding on its dynamics in an urban peridomestic cycle, a fractional-order derivative model is formulated and analysed. The basic reproduction number ℛ 0 is computed and used in analysing the stability of disease when an outbreak occurs. Numerical simulations are performed in order to the variation of each population at order α = 1,0.75 , 0.5 , and 0.25. Results from simulations show that there is an increase in susceptible and exposed population in both human and mosquitoes as the value of α decreases. The infected population decreases with a decrease in the value of α . However, a rapid increase in susceptible mosquitoes is observed just after the first 30 days and a rapid decrease in infected human and mosquitoes after the first 30 days for α = 1 . Hence, fractional-order derivative also plays a significant role in providing insight on disease transmission and dynamics.
Highlights
Rift Valley fever (RVF) is a mosquito-borne zoonotic viral disease which affects both humans and animals. e main causative agent of RVF is the Rift Valley fever virus (RVFV) of the genus Phlebovirus in the family Bunyaviridae [1]. e virus was first isolated in sheep in 1930 during an outbreak in Kenya [2]
Humans become infected mostly from contact with the blood or organs of infected animals, while, in the urban peridomestic cycle, humans become infected through the bites of mosquitoes [1]. e Egyptian outbreak of 1977-1978 is known to be peridomestic and anthropophilic [4]. ere are possibilities for human infections to result from other blood-feeding insects, which might be serve as mechanical transmitters of infection. e current urban peridomestic outbreaks of RVF include the 2019 outbreak in Sudan where 1,129 case patients and 19 deaths were reported [5] and that of Mayotte (France) where 143 human cases were reported [6]
A fractional-order derivative approach using Caputo derivative has been used to investigate the dynamics of RVF in an urban peridomestic cycle. e basic reproduction number R0 of the model was computed to study the effect of initial transmission of the disease and used to analyse the stability of the disease-free equilibrium and endemic equilibrium. e analysis of the stability of equilibrium points indicated that both the disease-free equilibrium and endemic equilibrium of the model system are locally and globally asymptotically stable. e stability of the disease-free equilibrium means that the RVF outbreak can be controlled provided that R0 < 1
Summary
Rift Valley fever (RVF) is a mosquito-borne zoonotic viral disease which affects both humans and animals. e main causative agent of RVF is the Rift Valley fever virus (RVFV) of the genus Phlebovirus in the family Bunyaviridae [1]. e virus was first isolated in sheep in 1930 during an outbreak in Kenya [2]. Rift Valley fever (RVF) is a mosquito-borne zoonotic viral disease which affects both humans and animals. E main causative agent of RVF is the Rift Valley fever virus (RVFV) of the genus Phlebovirus in the family Bunyaviridae [1]. Domestic animals are highly susceptible to RVFV infection and are considered to be the major amplifiers of the virus [3]. E transmission of RVFV to humans can result through different cycles: the sylvatic cycle and the urban peridomestic cycle [1]. Humans become infected mostly from contact with the blood or organs of infected animals, while, in the urban peridomestic cycle, humans become infected through the bites of mosquitoes [1]. Humans become infected mostly from contact with the blood or organs of infected animals, while, in the urban peridomestic cycle, humans become infected through the bites of mosquitoes [1]. e Egyptian outbreak of 1977-1978 is known to be peridomestic and anthropophilic [4]. ere are possibilities for human infections to result from other blood-feeding insects, which might be serve as mechanical transmitters of infection. e current urban peridomestic outbreaks of RVF include the 2019 outbreak in Sudan where 1,129 case patients and 19 deaths were reported [5] and that of Mayotte (France) where 143 human cases were reported [6]
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